The -dimensional elliptic Toda equation is a higher dimensional generalization of the Toda lattice and also a discrete version of the Kadomtsev-Petviashvili-1 (KP1) equation. In this paper, we derive the -breather solution in the determinant form for the -dimensional elliptic Toda equation via Bäcklund transformation and nonlinear superposition formulae. The lump solutions of the -dimensional elliptic

Fractional diffusion on the sphere plays a large role in the study of physical phenomena customs and meteorology and geophysics. In this paper, we examine two types of the sphere problem: the initial value problem and the end value problem. We are interested in focus on the solution existence in a local or global form. In order to overcome difficult evaluations when evaluating, we need some new techniques

In this paper, we present a class of numerical schemes and apply it to the diffusion equations. The objective is to obtain numerical solutions of the constructive equations of a type of Casson fluid model. We investigate the solutions of the free convection flow of the Casson fluid along with heat and mass transfer in the context of modeling with the fractional operators. The numerical scheme presented

In this paper, the notion of sequential -metric spaces has been introduced as a generalization of usual -metric spaces, -metric spaces, metric spaces, and specially of -metric spaces. In view of this notion, we prove some fixed point theorems for some classes of -rational Geraghty JS-contractions over such spaces. A supporting example and an application have been given in order to examine the validity

In this paper, we study the following nonlocal problem where are constants, , , is a positive function, and is a smooth bounded domain in with . By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided is small enough.

In this paper, we establish strong and convergence results for mappings satisfying condition through a newly introduced iterative process called JA iteration process. A nonlinear Hadamard space is used the ground space for establishing our main results. A novel example is provided for the support of our main results and claims. The presented results are the good extension of the corresponding results

In this paper, our leading objective is to relate the fractional integral operator known as -transform with the -extended Mathieu series. We show that the -transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in

In this study, analytical examination of effects of internal heat generation, thermal radiation, and buoyancy force on flow and heat transfer in the Blasius flow over flat plate has been presented. The governing nonlinear partial differential equations of the problem are transformed into a set of coupled nonlinear third-order ordinary differential equations by the similarity variable method and have

In this paper, with the aid of symbolic computation system Python and based on the deep neural network (DNN), automatic differentiation (AD), and limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization algorithms, we discussed the modified Korteweg-de Vries (mkdv) equation to obtain numerical solutions. From the predicted solution and the expected solution, the resulting prediction error

The exact traveling wave solution of the fractional Sharma-Tasso-Olever equation can be obtained by using the function expansion method, but the general traveling wave solution cannot be obtained. After transforming it into the Sharma-Tasso-Olever equation of the integer order by the fractional complex transformation, the general solution of its traveling wave is obtained by a specific function transformation

Under investigation in this paper is the higher-order Broer-Kaup(HBK) system, which describes the bidirectional propagation of long waves in shallow water. Via the standard truncated Painlevé expansion method, the residual symmetry of this system is derived. By introducing an appropriate auxiliary-dependent variable, the residual symmetry is successfully localized to Lie point symmetries. Via solving

The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. The solution of the governing equations is found using integral transformations

In this paper, we investigate the solutions of coupled fractional pantograph differential equations with instantaneous impulses. The work improves some existing results and contributes toward the development of the fractional differential equation theory. We first provide some definitions that will be used throughout the paper; after that, we give the existence and uniqueness results that are based

By -soliton solutions and a velocity resonance mechanism, soliton molecules are constructed for the KdV-Sawada-Kotera-Ramani (KSKR) equation, which is used to simulate the resonances of solitons in one-dimensional space. An asymmetric soliton can be formed by adjusting the distance between two solitons of soliton molecule to small enough. The interactions among multiple soliton molecules for the equation

We study the Cauchy problem of the three-dimensional full compressible Euler equations with damping and heat conduction. We prove the existence and uniqueness of the global small solution; in particular, we only require that the norms of the initial data be small when . Moreover, we use a pure energy method to show that the global solution converges to the constant equilibrium state with an optimal

A general coupled KdV equation, which describes the interactions of two long waves with different dispersion relation, is considered. By employing the Hirota’s bilinear method, the bilinear form is obtained, and the one-soliton solution and two-soliton solution are constructed. Moreover, the elasticity of the collision between two solitons is proved by analyzing the asymptotic behavior of the two-soliton

In this article, the concept of sequential -metric spaces has been introduced as a generalization of usual metric spaces, -metric spaces, -metric spaces, and mainly -metric spaces. Some topological properties of such spaces have been discussed here. By considering this notion, we prove fixed-point theorems for some classes of contractive mappings over such spaces. Examples have been given in order

The modified short-wave equation is considered under periodic boundary condition. We prove the global existence of solution with finite energy. We also find traveling wave solutions which is the form of elliptic function.

The dynamics of rotating objects is an area of classical mechanics that has many unsolved problems. Among these problems are the gyroscopic effects manifested by the spinning objects of different forms. One of them is the Tippe top designed as the truncated sphere which is fitted with a short, cylindrical rod for rotation. The unexplainable gyroscopic effect of the Tippe top is manifested by its inversion

In this paper, the reduced differential transform method (RDTM) is successfully implemented for solving two-dimensional nonlinear sine-Gordon equations subject to appropriate initial conditions. Some lemmas which help us to solve the governing problem using the proposed method are proved. This scheme has the advantage of generating an analytical approximate solution or exact solution in a convergent

In this paper, we investigate breather positons and higher-order rogue waves for the nonlocal Fokas-Lenells equation. In this nonlocal optical system, rogue waves can be generated when periods of breather positons go to infinity. In addition, we find two very interesting phenomena: one is that rogue waves sitting on a periodic line wave background are derived; the other is that a hybrid of rogue waves

In this study, we deal with the problem of constructing semianalytical solution of mathematical problems including space-time-fractional linear and nonlinear differential equations. The method, called Shehu Variational Iteration Method (SVIM), applied in this study is a combination of Shehu transform (ST) and variational iteration method (VIM). First, ST is utilized to reduce the time-fractional differential

This article intends to review quasirandom sequences, especially the Faure sequence to introduce a new version of scrambled of this sequence based on irrational numbers, as follows to prove the success of this version of the random number sequence generator and use it in future calculations. We introduce this scramble of the Faure sequence and show the performance of this sequence in employed numerical

The time-scale version of Noether symmetry and conservation laws for three Birkhoffian mechanics, namely, nonshifted Birkhoffian systems, nonshifted generalized Birkhoffian systems, and nonshitfed constrained Birkhoffian systems, are studied. Firstly, on the basis of the nonshifted Pfaff-Birkhoff principle on time scales, Birkhoff’s equations for nonshifted variables are deduced; then, Noether’s quasi-symmetry

In this article, we discuss the existence and uniqueness of solutions for a new class of coupled system of sequential fractional differential equations involving -Hilfer fractional derivatives, supplemented with multipoint boundary conditions. We make use of Banach’s fixed point theorem to obtain the uniqueness result and the Leray-Schauder alternative to obtain the existence result. Examples illustrating

Squeezing and entanglement of a two-mode cascade laser, produced by a three-level atom which is initially prepared by a coherent superposition of the top and bottom levels then injected into a cavity coupled to a two-mode squeezed vacuum reservoir is discussed. I obtain stochastic differential equations associated with the normal ordering using the pertinent master equation. Making use of the solutions

In this paper, the Kudryashov method to construct the new exact solitary wave solutions for the newly developed ()-dimensional Benjamin-Ono equation is successfully employed. In the same vein, also the new ()-dimensional Benjamin-Ono equation to ()-dimensional spaces is extended and then analyzed and investigated. Different forms of exact solitary wave solutions to this new equation were also determined

In this paper, we classified the paracontact metric -manifold satisfying the Miao-Tam critical equation with . We proved that it is locally isometric to the product of a flat -dimensional manifold and an -dimensional manifold of negative constant curvature .

In a rectangular region, the multilayered laminar unsteady flow and temperature distribution of the immiscible Maxwell fractional fluids by two parallel moving walls are studied. The flow of the fluid occurs in the presence of Robin’s boundaries and linear fluid-fluid interface conditions due to the motion of the parallel walls on its planes and the time-dependent pressure gradient. The problem is

Our aim is to establish a tripled fixed and coincidence point result on generalized -algebra-valued metric spaces. We present an example on matrices. At the end, we give an application on integral equations.

The purpose of this article is to study numerically the Turing diffusion-driven instability mechanism for pattern formation on curved surfaces embedded in , specifically the surface of the sphere and the torus with some well-known kinetics. To do this, we use Euler’s backward scheme for discretizing time. For spatial discretization, we parameterize the surface of the torus in the standard way, while

Three nonlinear fractional models, videlicet, the space-time fractional Boussinesq equation, -dimensional breaking soliton equations, and SRLW equation, are the important mathematical approaches to elucidate the gravitational water wave mechanics, the fractional quantum mechanics, the theoretical Huygens’ principle, the movement of turbulent flows, the ion osculate waves in plasma physics, the wave

The soliton molecules, as bound states of solitons, have attracted considerable attention in several areas. In this paper, the -dimensional higher-order Boussinesq equation is constructed by introducing two high-order Hirota operators in the usual -dimensional Boussinesq equation. By the velocity resonance mechanism, the soliton molecule and the asymmetric soliton of the higher-order Boussinesq equation

In this manuscript, we consider the fourth order of the Moore–Gibson–Thompson equation by using Galerkin’s method to prove the solvability of the given nonlocal problem.

This paper discusses a boundary value problem of nonlinear fractional integrodifferential equations of order and and boundary conditions of the form . Some new existence and uniqueness results are proposed by using the fixed point theory. In particular, we make use of the Banach contraction mapping principle and Krasnoselskii’s fixed point theorem under some weak conditions. Moreover, two illustrative

In this paper, we study the different types of new soliton solutions to the Landau–Lifshitz equation with the aid of the auxiliary equation method. Then, we get some special soliton solutions for this equation. Without the Gilbert damping term, we present a travelling wave solution with a finite energy in the initial time. The parameters of the soliton envelope are obtained as a function of the dependent

The equation of motion in of generalized point charges interacting via the -dimensional Coulomb potential, which contains for a constant magnetic field, is considered. Planar exact solutions of the equation are found if either negative charges and their masses are equal or and the charges are different. They describe a motion of negative charges along identical orbits around the positive immobile charge

Based on the bilinear method, rational lump and mixed lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation are constructed through the different assumptions of the auxiliary function in the trilinear form. It is found that the rational lump decays algebraically in all directions in the space plane and its amplitude possesses one maximum and two minima. One kind of the mixed solution

In this paper, the motion of a rigid body in a singular case of the natural frequency () is considered. This case of singularity appears in the previous works due to the existence of the term in the denominator of the obtained solutions. For this reason, we solve the problem from the beginning. We assume that the body rotates about its fixed point in a Newtonian force field and construct the equations

In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the and axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of

We investigate a motion of the incompressible 2D-MHD with power law-type nonlinear viscous fluid. In this paper, we establish the global existence and uniqueness of a weak solution depending on a number in . Moreover, the energy norm of the weak solutions to the fluid flows has decay rate .

We analyze a nondegenerate three-level cascade laser with an open cavity and coupled to a two-mode thermal reservoir employing the stochastic differential equations for atomic operators associated with the normal ordering. Applying the large-time approximation scheme, we obtain the solutions for the corresponding equations of evolution of the expectation values of atomic operators. Furthermore, employing

In this paper, the boundary value inverse problem related to the generalized Burgers–Fisher and generalized Burgers–Huxley equations is solved numerically based on a spline approximation tool. B-splines with quasilinearization and Tikhonov regularization methods are used to obtain new numerical solutions to this problem. First, a quasilinearization method is used to linearize the equation in a specific

In this paper, a beta operator is used with Caputo Marichev-Saigo-Maeda (MSM) fractional differentiation of extended Mittag-Leffler function in terms of beta function. Further in this paper, some corollaries and consequences are shown that are the special cases of our main findings. We apply the beta operator on the right-sided MSM fractional differential operator and on the left-sided MSM fractional

This paper deals with the existence of solutions for a new class of nonlinear fractional boundary value systems involving the left and right Riemann-Liouville fractional derivatives. More precisely, we establish the existence of at least three weak solutions for the problem using variational methods combined with the critical point theorem due to Bonano and Marano. In addition, some examples in and

This paper is devoted to the initial and boundary value problems for a class of nonlinear metaparabolic equations . At low initial energy level (), we not only prove the existence of global weak solutions for these problems by the combination of the Galerkin approximation and potential well methods but also obtain the finite time blow-up result by adopting the potential well and improved concavity

In this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. The performances of these new methods and Hardy Cross method were compared by solving

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

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

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

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

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

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.

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.

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

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”

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

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

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.

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.