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Three-Dimensional Simulations of Offshore Oil Platform in Square and Diamond Arrangements Adv. Math. Phys. (IF 1.13) Pub Date : 2021-03-02 Saliha Nouri; Zouhair Hafsia; Salah Mahmoud Boulaaras; Ali Allahem; Salem Alkhalaf; Aldo Munoz Vazquez
The interaction of the solitary wave with an oil platform composed of four vertical circular cylinders is investigated for two attack angle of the solitary wave (square arrangement) and (diamond arrangement). The solitary wave is generated using an internal source line as proposed by Hafsia et al. (2009). This generation method is extended to three-dimensional wave flow and is integrated into the PHOENICS
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Novel Numerical Scheme for Singularly Perturbed Time Delay Convection-Diffusion Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-28 Mesfin Mekuria Woldaregay; Worku Tilahun Aniley; Gemechis File Duressa
This paper deals with numerical treatment of singularly perturbed parabolic differential equations having large time delay. The highest order derivative term in the equation is multiplied by a perturbation parameter , taking arbitrary value in the interval . For small values of , solution of the problem exhibits an exponential boundary layer on the right side of the spatial domain. The properties and
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Some Convergence Results for a Class of Generalized Nonexpansive Mappings in Banach Spaces Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-27 Thabet Abdeljawad; Kifayat Ullah; Junaid Ahmad; Manuel de la Sen; Muhammad Naveed Khan
This paper investigates fixed points of Reich-Suzuki-type nonexpansive mappings in the context of uniformly convex Banach spaces through an iterative method. Under some appropriate situations, some strong and weak convergence theorems are established. To support our results, a new example of Reich-Suzuki-type nonexpansive mappings is presented which exceeds the class of Suzuki-type nonexpansive mappings
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Line Soliton Interactions for Shallow Ocean Waves and Novel Solutions with Peakon, Ring, Conical, Columnar, and Lump Structures Based on Fractional KP Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-27 Bo Xu; Yufeng Zhang; Sheng Zhang
It is well known that the celebrated Kadomtsev-Petviashvili (KP) equation has many important applications. The aim of this article is to use fractional KP equation to not only simulate shallow ocean waves but also construct novel spatial structures. Firstly, the definitions of the conformable fractional partial derivatives and integrals together with a physical interpretation are introduced and then
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Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-23 Chao Yue; Guijuan Liu; Kun Li; Hanhui Dong
By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional Harry Dym equation is presented. Furthermore, numerical solutions of time-fractional diffusion equation are discussed. Again, through another similarity
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Extinction Phenomenon and Decay Estimate for a Quasilinear Parabolic Equation with a Nonlinear Source Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-20 Dengming Liu; Luo Yang
By energy estimate approach and the method of upper and lower solutions, we give the conditions on the occurrence of the extinction and nonextinction behaviors of the solutions for a quasilinear parabolic equation with nonlinear source. Moreover, the decay estimates of the solutions are studied.
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A New Result for a Blow-up of Solutions to a Logarithmic Flexible Structure with Second Sound Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-11 Ahlem Merah; Fatiha Mesloub; Salah Mahmoud Boulaaras; Bahri-Belkacem Cherif
This paper is concerned with a problem of a logarithmic nonuniform flexible structure with time delay, where the heat flux is given by Cattaneo’s law. We show that the energy of any weak solution blows up infinite time if the initial energy is negative.
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The Stochastic Resonance Phenomenon of Different Noises in Underdamped Bistable System Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-11 Shan Yang; Zening Fan; Ruibin Ren
In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention
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Logarithmic Generalization of the Lambert Function and Its Applications to Adiabatic Thermostatistics of the Three-Parameter Entropy Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-09 Cristina B. Corcino; Roberto B. Corcino
A generalization of the Lambert function called the logarithmic Lambert function is introduced and is found to be a solution to the thermostatistics of the three-parameter entropy of classical ideal gas in adiabatic ensembles. The derivative, integral, Taylor series, approximation formula, and branches of the function are obtained. The heat functions and specific heats are computed using the “unphysical”
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Uncertain Random Data Envelopment Analysis: Efficiency Estimation of Returns to Scale Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-08 Bao Jiang; Shuang Feng; Jinwu Gao; Jian Li
Evaluating efficiency according to the different states of returns to scale (RTS) is crucial to resource allocation and scientific decision for decision-making units (DMUs), but this kind of evaluation will become very difficult when the DMUs are in an uncertain random environment. In this paper, we attempt to explore the uncertain random data envelopment analysis approach so as to solve the problem
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Painlevé Analysis, Soliton Molecule, and Lump Solution of the Higher-Order Boussinesq Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-04 Bo Ren
The Painlevé integrability of the higher-order Boussinesq equation is proved by using the standard Weiss-Tabor-Carnevale (WTC) method. The multisoliton solutions of the higher-order Boussinesq equation are obtained by introducing dependent variable transformation. The soliton molecule and asymmetric soliton of the higher-order Boussinesq equation can be constructed by the velocity resonance mechanism
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Periodic Peakon and Smooth Periodic Solutions for KP-MEW(3,2) Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-03 Junning Cai; Minzhi Wei; Liping He
In this paper, we consider the KP-MEW(3,2) equation by the bifurcation theory of dynamical systems when integral constant is considered. The corresponding traveling wave system is a singular planar dynamical system with one singular straight line. The phase portrait for , , and is drawn. Exact parametric representations of periodic peakon solutions and smooth periodic solution are presented.
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On -Cone Metric Spaces over a Banach Algebra and Some Fixed-Point Theorems Adv. Math. Phys. (IF 1.13) Pub Date : 2021-02-01 Jerolina Fernandez; Neeraj Malviya; Vahid Parvaneh; Hassen Aydi; Babak Mohammadi
In the present paper, we define -cone metric spaces over a Banach algebra which is a generalization of -metric space (-MS) and cone metric space (CMS) over a Banach algebra. We give new fixed-point theorems assuring generalized contractive and expansive maps without continuity. Examples and an application are given at the end to support the usability of our results.
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An Interpolation Theorem for Quasimartingales in Noncommutative Symmetric Spaces Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-31 Congbian MA; Guoxi Zhao
Let be a separable symmetric space on and the corresponding noncommutative space. In this paper, we introduce a kind of quasimartingale spaces which is like but bigger than and obtain the following interpolation result: let be the space of all bounded -quasimartingales and . Then, there exists a symmetric space on with nontrivial Boyd indices such that .
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The Existence of Least Energy Sign-Changing Solution for Kirchhoff-Type Problem with Potential Vanishing at Infinity Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-31 Ting Xiao; Canlin Gan; Qiongfen Zhang
In this paper, we study the Kirchhoff-type equation: where , , , and . and are vanishing at infinity. With the aid of the quantitative deformation lemma and constraint variational method, we prove the existence of a sign-changing solution to the above equation. Moreover, we obtain that the sign-changing solution has exactly two nodal domains. Our results can be seen as an improvement of the previous
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Improvement of the Nonparametric Estimation of Functional Stationary Time Series Using Yeo-Johnson Transformation with Application to Temperature Curves Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-30 Sameera Abdulsalam Othman; Haithem Taha Mohammed Ali
In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series datasets of monthly temperature averages to improve the forecast ability. An application algorithm was proposed to transform the positive original responses using the first model and the stationary responses using the second model to improve the nonparametric estimation of the functional time series. The Box-Cox
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Interaction of Two-Level Atom with Squeezed Vacuum Reservoir Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-29 Tamirat Abebe; Demissie Jobir; Chimdessa Gashu; Ebisa Mosisa
In this paper, the quantum properties of a two-level atom interaction with squeezed vacuum reservoir is throughly analyzed. With the aid of the interaction Hamiltonian and the master equation, we obtain the time evolution of the expectation values of the atomic operators. Employing the steady-state solution of these equations, we calculate the power spectrum and the second-order correlation function
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Second-Order Conditional Lie-Bäcklund Symmetry and Differential Constraint of Radially Symmetric Diffusion System Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-18 Jianping Wang; Huijing Ba; Yaru Liu; Longqi He; Lina Ji
The classifications and reductions of radially symmetric diffusion system are studied due to the conditional Lie-Bäcklund symmetry method. We obtain the invariant condition, which is the so-called determining system and under which the radially symmetric diffusion system admits second-order conditional Lie-Bäcklund symmetries. The governing systems and the admitted second-order conditional Lie-Bäcklund
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Application of the Multiple Exp-Function, Cross-Kink, Periodic-Kink, Solitary Wave Methods, and Stability Analysis for the CDG Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-16 Haifa Bin Jebreen; Yurilev Chalco-Cano
In this article, the exact wave structures are discussed to the Caudrey-Dodd-Gibbon equation with the assistance of Maple based on the Hirota bilinear form. It is investigated that the equation exhibits the trigonometric, hyperbolic, and exponential function solutions. We first construct a combination of the general exponential function, periodic function, and hyperbolic function in order to derive
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Lax Representation and Darboux Solutions of the Classical Painlevé Second Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-15 Irfan Mahmood; Muhammad Waseem
In this article, we present Darboux solutions of the classical Painlevé second equation. We reexpress the classical Painlevé second Lax pair in new setting introducing gauge transformations to yield its Darboux expression in additive form. The new linear system of that equation carries similar structure as other integrable systems possess in the AKNS scheme. Finally, we generalize the Darboux transformation
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The Maschke-Type Theorem and Morita Context for BiHom-Smash Products Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-15 Bingliang Shen; Ling Liu
Let be a BiHom-Hopf algebra and be an -module BiHom-algebra. Then, in this paper, we study some properties on the BiHom-smash product . We construct the Maschke-type theorem for the BiHom-smash product and form an associated Morita context .
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New Exact Traveling Wave Solutions of the Time Fractional Complex Ginzburg-Landau Equation via the Conformable Fractional Derivative Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-08 Zhao Li; Tianyong Han
In this study, the exact traveling wave solutions of the time fractional complex Ginzburg-Landau equation with the Kerr law and dual-power law nonlinearity are studied. The nonlinear fractional partial differential equations are converted to a nonlinear ordinary differential equation via a traveling wave transformation in the sense of conformable fractional derivatives. A range of solutions, which
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Correlated Log-Normal Random Variables under a Multiscale Volatility Model Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-06 Yong-Ki Ma
The study focuses on extending the fast mean-reversion volatility, which was developed by the author in a previous work, to the multiscale volatility model so that it can express a well-separated time scale. The leading-order term and first-order correction terms are analytically computed using the perturbation theory based on the Lie–Trotter operator splitting method. Finally, the study is concluded
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Uniqueness of Complete Hypersurfaces in Weighted Riemannian Warped Products Adv. Math. Phys. (IF 1.13) Pub Date : 2021-01-02 Ning Zhang
In this paper, applying the weak maximum principle, we obtain the uniqueness results for the hypersurfaces under suitable geometric restrictions on the weighted mean curvature immersed in a weighted Riemannian warped product whose fiber has -parabolic universal covering. Furthermore, applications to the weighted hyperbolic space are given. In particular, we also study the special case when the ambient
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Analytic Treatment for Electrical MHD Non-Newtonian Fluid Flow over a Stretching Sheet through a Porous Medium Adv. Math. Phys. (IF 1.13) Pub Date : 2020-12-28 Gossaye Aliy Adem
In this study, an attempt has been made to investigate the mass and heat transfer effects in a BLF through a porous medium of an electrically conducting viscoelastic fluid subject to a transverse magnetic field in the existence of an external electric field, heat source/sink, and chemical reaction. It has been considered the effects of the electric field, viscous and Joule dissipations, radiation,
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Vector Solutions for Linearly Coupled Choquard Type Equations with Lower Critical Exponents Adv. Math. Phys. (IF 1.13) Pub Date : 2020-12-21 Huiling Wu
The existence, nonexistence, and multiplicity of vector solutions of the linearly coupled Choquard type equations are proved, where , , are positive functions, and denotes the Riesz potential.
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Finite-Time Antisynchronization and Parameters Identification of Nonlinear Coupled Multiple-Weight Markovian Switching Complex Networks with Stochastic Perturbations Adv. Math. Phys. (IF 1.13) Pub Date : 2020-12-11 Haifeng Qiu; Liguo Weng; Bin Yu; Yanghui Zhang
The paper mainly focuses on the synchronization of multiple-weight Markovian switching complex networks under nonlinear coupling mode. Based on the finite-time stability theory, Itô’s lemma, and some inequality technologies, the synchronization criterion of network models in the nonlinear coupling mode is obtained; at the same time, unknown parameters of networks are also identified by an effective
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Fixed-Point Results for Generalized -Admissible Hardy-Rogers’ Contractions in Cone -Metric Spaces over Banach’s Algebras with Application Adv. Math. Phys. (IF 1.13) Pub Date : 2020-12-08 Ziaul Islam; Muhammad Sarwar; Manuel de la Sen
In the current manuscript, the notion of a cone -metric space over Banach’s algebra with parameter is introduced. Furthermore, using -admissible Hardy-Rogers’ contractive conditions, we have proven fixed-point theorems for self-mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application
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The Motion of a Rigid Body with Irrational Natural Frequency Adv. Math. Phys. (IF 1.13) Pub Date : 2020-12-07 A. I. Ismail
In this paper, we consider the problem of the rotational motion of a rigid body with an irrational value of the frequency . The equations of motion are derived and reduced to a quasilinear autonomous system. Such system is reduced to a generating one. We assume a large parameter proportional inversely with a sufficiently small component of the angular velocity which is assumed around the major or the
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Theory of B(X)-Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-29 Yoritaka Iwata
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators. In conclusion, the concept of module over a Banach algebra is
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Existence and Large Time Behavior of Entropy Solutions to One-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-23 Yan Li; Yanqiu Cheng; Huimin Yu
In this paper, we investigate the global existence and large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Possion equations with time and spacedependent damping in a bounded interval. Firstly, we prove the existence of entropy solutions through vanishing viscosity method and compensated compactness framework. Based on the
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Fixed-Point Theorem for Nonlinear -Contraction via -Distance Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-19 Abdelkarim Kari; Mohamed Rossafi; El Miloudi Marhrani; Mohamed Aamri
The aim of this paper is to introduce a notion of -contraction defined on a metric space with -distance. Moreover, fixed-point theorems are given in this framework. As an application, we prove the existence and uniqueness of a solution for the nonlinear Fredholm integral equations. Some illustrative examples are provided to advocate the usability of our results.
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Exact Analytical Solutions of Nonlinear Fractional Liouville Equation by Extended Complex Method Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-19 Mehvish Fazal Ur Rehman; Yongyi Gu; Wenjun Yuan
The extended complex method is investigated for exact analytical solutions of nonlinear fractional Liouville equation. Based on the work of Yuan et al., the new rational, periodic, and elliptic function solutions have been obtained. By adjusting the arbitrary values to the constants in the constructed solutions, it can describe the physical phenomena to the traveling wave solutions, since traveling
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A Riemann-Hilbert Approach to the Multicomponent Kaup-Newell Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-18 Jian-bing Zhang; Ze-xuan Zhang
A Riemann-Hilbert approach is developed to the multicomponent Kaup-Newell equation. The formula is presented of -soliton solutions through an identity jump matrix related to the inverse scattering problems with reflectionless potential.
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An Extended -Metric-Type Space and Related Fixed Point Theorems with an Application to Nonlinear Integral Equations Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-17 Kushal Roy; Sayantan Panja; Mantu Saha; Vahid Parvaneh
In this paper, the concept of sequential -metric spaces has been introduced as a generalization of usual metric spaces, -metric spaces and specially of -metric spaces. Several topological properties of such spaces have been discussed here. In view of this notion, we prove fixed point theorems for some classes of contractive mappings over such spaces. Supporting examples have been given in order to
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Study of Dust-Acoustic Multisoliton Interactions in Strongly Coupled Dusty Plasmas Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-16 Najah Kabalan; Mahmoud Ahmad; Ali Asad
The effect of the structure parameter on the compressibility of dust grains and soliton behavior in a dusty plasma system consisting of Maxwellian electrons, ions, and dust grains charged with a negative charge has been studied. In the theoretical study, a reductive perturbation technique was used to derive the Korteweg-de Vries (KdV) equation and employ the Hirota bilinear method to obtain multisoliton
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Long-Range Scalar Forces in Five-Dimensional General Relativity Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-09 L. L. Williams
We present new results regarding the long-range scalar field that emerges from the classical Kaluza unification of general relativity and electromagnetism. The Kaluza framework reproduces known physics exactly when the scalar field goes to one, so we studied perturbations of the scalar field around unity, as is done for gravity in the Newtonian limit of general relativity. A suite of interesting phenomena
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New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-09 Yu-Ming Chu; Shumaila Javeed; Dumitru Baleanu; Sidra Riaz; Hadi Rezazadeh
This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). The suggested technique is implemented to obtain the solutions of space-time Kolmogorov Petrovskii Piskunov (KPP) equation and its derived equations, namely, Fitzhugh Nagumo (FHN) equation and Newell-Whitehead (NW)
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Existence Results for a Class of Coupled Hilfer Fractional Pantograph Differential Equations with Nonlocal Integral Boundary Value Conditions Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-06 Karim Guida; Khalid Hilal; Lahcen Ibnelazyz
This paper deals with the existence and uniqueness of solutions for a new class of coupled systems of Hilfer fractional pantograph differential equations with nonlocal integral boundary conditions. First of all, we are going to give some definitions that are necessary for the understanding of the manuscript; second of all, we are going to prove our main results using the fixed point theorems, namely
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Analytical Method for Solving the Fractional Order Generalized KdV Equation by a Beta-Fractional Derivative Adv. Math. Phys. (IF 1.13) Pub Date : 2020-11-04 Majid Bagheri; Ali Khani
The present work is related to solving the fractional generalized Korteweg-de Vries (gKdV) equation in fractional time derivative form of order . Some exact solutions of the fractional-order gKdV equation are attained by employing the new powerful expansion approach by using the beta-fractional derivative which is used to get many solitary wave solutions by changing various parameters. The obtained
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On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-30 Ahmed Salem; Noorah Mshary
In this work, we give sufficient conditions to investigate the existence and uniqueness of solution to fractional-order Langevin equation involving two distinct fractional orders with unprecedented conditions (three-point boundary conditions including two nonlocal integrals). The problem is introduced to keep track of the progress made on exploring the existence and uniqueness of solution to the fractional-order
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Positive Solutions Depending on Parameters for a Nonlinear Fractional System with -Laplacian Operators Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-30 Chen Yang; Xiaolin Zhu
This paper considers a system of fractional differential equations involving -Laplacian operators and two parameters where , , and are the standard Riemann-Liouville derivatives, , , , , and and and are two positive parameters. We obtain the existence and uniqueness of positive solutions depending on parameters for the system by utilizing a recent fixed point theorem. Furthermore, an example is present
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Adaptive High-Order Finite Difference Analysis of 2D Quenching-Type Convection-Reaction-Diffusion Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-29 Xiaoliang Zhu; Yongbin Ge
Quenching characteristics based on the two-dimensional (2D) nonlinear unsteady convection-reaction-diffusion equation are creatively researched. The study develops a 2D compact finite difference scheme constructed by using the first and the second central difference operator to approximate the first-order and the second-order spatial derivative, Taylor series expansion rule, and the reminder-correction
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Variational Approach for the Variable-Order Fractional Magnetic Schrödinger Equation with Variable Growth and Steep Potential in Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-28 Jianwen Zhou; Bianxiang Zhou; Liping Tian; Yanning Wang
In this paper, we show the existence of solutions for an indefinite fractional Schrödinger equation driven by the variable-order fractional magnetic Laplace operator involving variable exponents and steep potential. By using the decomposition of the Nehari manifold and variational method, we obtain the existence results of nontrivial solutions to the equation under suitable conditions.
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Hidden Multistability in a Memristor-Based Cellular Neural Network Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-27 Birong Xu; Hairong Lin; Guangyi Wang
In this paper, we report a novel memristor-based cellular neural network (CNN) without equilibrium points. Dynamical behaviors of the memristor-based CNN are investigated by simulation analysis. The results indicate that the system owns complicated nonlinear phenomena, such as hidden attractors, coexisting attractors, and initial boosting behaviors of position and amplitude. Furthermore, both heterogeneous
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On Analytical Solution of a Plasma Flow over a Moving Plate under the Effect of an Applied Magnetic Field Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-22 Taha Zakaraia Abdel Wahid; Adel M. Morad
Our objective of this investigation is to mainly focus on the behavior of a plasma gas that is bounded by a moving rigid flat plate; its motion is damping with time. The effects of an external magnetic field on the electrons collected with each other, with positive ions, and with neutral atoms in the plasma fluid are studied. The BGK type of the Boltzmann kinetic equation is used to study the gas dynamics
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On the Fractional Derivative of Dirac Delta Function and Its Application Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-20 Zaiyong Feng; Linghua Ye; Yi Zhang
The Dirac delta function and its integer-order derivative are widely used to solve integer-order differential/integral equation and integer-order system in related fields. On the other hand, the fractional-order system gets more and more attention. This paper investigates the fractional derivative of the Dirac delta function and its Laplace transform to explore the solution for fractional-order system
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Fractal Ion Acoustic Waves of the Space-Time Fractional Three Dimensional KP Equation Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-17 M. A. Abdou; Saud Owyed; S. Saha Ray; Yu-Ming Chu; Mustafa Inc; Loubna Ouahid
Methods known as fractional subequation and sine-Gordon expansion (FSGE) are employed to acquire new exact solutions of some fractional partial differential equations emerging in plasma physics. Fractional operators are employed in the sense of conformable derivatives (CD). New exact solutions are constructed in terms of hyperbolic, rational, and trigonometric functions. Computational results indicate
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Coherently Driven Number of Degenerate Three-Level Atoms with Parametric Amplifier Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-12 Tamirat Abebe; Chimdessa Gashu; Nebiyu Gemechu
We have analyzed the squeezing and statistical properties of the cavity light beam produced by a coherently driven degenerate three-level laser with a degenerate parametric amplifier (DPA) in an open cavity and coupled to a vacuum reservoir via a single-port mirror. We have carried out our analysis by putting the noise operators associated with the vacuum reservoir in normal order. Applying the solutions
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Quasi-Einstein Hypersurfaces of Complex Space Forms Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-12 Xiaomin Chen; Xuehui Cui
Based on a well-known fact that there are no Einstein hypersurfaces in a nonflat complex space form, in this article, we study the quasi-Einstein condition, which is a generalization of an Einstein metric, on the real hypersurface of a nonflat complex space form. For the real hypersurface with quasi-Einstein metric of a complex Euclidean space, we also give a classification. Since a gradient Ricci
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High-Order Approximation to Two-Level Systems with Quasiresonant Control Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-06 Lin Wang; Jian Zu
In this paper, we focus on high-order approximate solutions to two-level systems with quasi-resonant control. Firstly, we develop a high-order renormalization group (RG) method for Schrödinger equations. By this method, we get the high-order RG approximate solution in both resonance case and out of resonance case directly. Secondly, we introduce a time transformation to avoid the invalid expansion
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Numerical Simulation and Symmetry Reduction of a Two-Component Reaction-Diffusion System Adv. Math. Phys. (IF 1.13) Pub Date : 2020-10-05 Jina Li; Xuehui Ji
In this paper, the symmetry classification and symmetry reduction of a two-component reaction-diffusion system are investigated, the reaction-diffusion system can be reduced to system of ordinary differential equations, and the solutions and numerical simulation will be showed by examples.
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Weakly Coupled B-Type Kadomtsev-Petviashvili Equation: Lump and Rational Solutions Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-30 Na Xiong; Wen-Tao Li; Biao Li
Through the method of -KP hierarchy, we propose a new ()-dimensional weakly coupled B-KP equation. Based on the bilinear form, we obtain the lump and rational solutions to the dimensionally reduced cases by constructing a symmetric positive semidefinite matrix. Then, we do numerical analysis on the rational solutions and fit the trajectory equation of the crest. Furthermore, we verify the accuracy
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Mechanical Solving a Few Fractional Partial Differential Equations and Discussing the Effects of the Fractional Order Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-30 Kai Fan; Cunlong Zhou
With the help of Maple, the precise traveling wave solutions of three fractal-order model equations related to water waves, including hyperbolic solutions, trigonometric solutions, and rational solutions, are obtained by using function expansion method. An isolated wave solution is selected from the solution of each nonlinear dispersive wave model equation, and the influence of fractional order change
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A Common Fixed Point Theorem for Nonlinear Quasi-Contractions on -Metric Spaces with Application in Integral Equations Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-29 Zoran D. Mitrović; Ivan D. Aranđelović; Vesna Mišić; Abdollah Dinmohammadi; Vahid Parvaneh
In this paper, we present a common fixed point result for a pair of mappings defined on a b-metric space, which satisfies quasi-contractive inequality with nonlinear comparison functions. An application in solving a class of integral equations will support our results.
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Existence of Mild Solutions for a Class of Impulsive Hilfer Fractional Coupled Systems Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-29 Karim Guida; Khalid Hilal; Lahcen Ibnelazyz
The aim of this paper is to give existence results for a class of coupled systems of fractional integrodifferential equations with Hilfer fractional derivative in Banach spaces. We first give some definitions, namely the Hilfer fractional derivative and the Hausdorff’s measure of noncompactness and the Sadovskii’s fixed point theorem.
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Torus and Subharmonic Motions of a Forced Vibration System in 1 : 5 Weak Resonance Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-26 Yong Guo
The Neimark-Sacker bifurcation of a forced vibration system is considered in this paper. The series solution to the motion equation is obtained, and the Poincaré map is established. The fixed point of the Poincaré map is guaranteed by the implicit function theorem. The map is transformed into its normal form at the fifth-order resonance case. For some parameter values, there exists the torus . Furthermore
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Adaptive Multilevel Collaborative Passenger Flow Control in Peak Hours for a Subway Line Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-24 Hongjiao Xue; Limin Jia; Jianyuan Guo
Due to contradiction of large-scale passenger demand and limited transportation capacity, the passengers who cannot be transported away in time accumulate and congest in stations. To ensure travel safety, improve travel efficiency, and ameliorate waiting environments for passengers, this paper proposes an adaptive multilevel collaborative passenger flow control strategy integrating the control of station
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On the Analytical and Numerical Solutions in the Quantum Magnetoplasmas: The Atangana Conformable Derivative ()-ZK Equation with Power-Law Nonlinearity Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-23 Mostafa M. A. Khater; Yu-Ming Chu; Raghda A. M. Attia; Mustafa Inc; Dianchen Lu
In this research paper, our work is connected with one of the most popular models in quantum magnetoplasma applications. The computational wave and numerical solutions of the Atangana conformable derivative ()-Zakharov-Kuznetsov (ZK) equation with power-law nonlinearity are investigated via the modified Khater method and septic-B-spline scheme. This model is formulated and derived by employing the
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Constraint and Nonlinearization of Supersymmetric Equations with Some Special Forms of Lax Pairs Adv. Math. Phys. (IF 1.13) Pub Date : 2020-09-22 Hongmin Li
We study the null boundary problems of some classical evolution equations constrained by some special forms of Lax pairs. Furthermore, we present the constraint and nonlinearization of some supersymmetric (SUSY) equations with a special form of Lax pairs and solve the null boundary problems of these SUSY equations under the corresponding constraints.
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