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Robust model predictive control for fractional-order descriptor systems with uncertainty Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-12-01 Adnène Arbi
In this study, a new robust predictive control technique is investigated for uncertain fractional-order descriptor systems. Using the properties of fractional calculus and the construction of an appropriate Lyapunov function, the sufficient conditions to guarantee the existence of a robust predictive controller are given by minimizing the worst-case optimization problem. The new robust predictive controller
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On the Fractional Dunkl–Laplacian Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-29 Fethi Bouzeffour, Wissem Jedidi
In this paper, we introduce a novel approach to the fractional Dunkl–Laplacian within a framework derived from specific reflection symmetries in Euclidean spaces. Our primary contributions include pointwise formulas, Bochner subordination, and addressing an extension problem for the fractional Dunkl–Laplacian.
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Least energy sign-changing solutions for fractional critical Kirchhoff–Schrödinger–Poisson with steep potential well Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-28 Shenghao Feng, Jianhua Chen, Jijiang Sun, Xianjiu Huang
In this paper, we consider the following Kirchhoff-Schrödinger-Poisson equation: $$\begin{aligned} \begin{aligned} \left\{ \begin{array}{lc} \left( a+b[u]_s^2\right) (-\varDelta )^s u+V_\lambda (x) u+\phi u=|u|^{p-2}u+|u|^{2_s^*-2} u &{}{} \text { in } {\mathbb {R}}^3, \\ (-\varDelta )^t \phi =u^2 &{}{} \text { in } {\mathbb {R}}^3, \end{array}\right. \end{aligned} \end{aligned}$$ where \(s \in \left(
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Time optimal controls for Hilfer fractional evolution equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-21 Yue Liang
This article investigates time optimal controls for the Cauchy problem of Hilfer fractional evolution equations. At first, by employing the fixed point technique and the operator semigroup theory, an existence theorem is obtained. Then the existence of time optimal control pair is studied by applying an approximate technique. An example is given as applications in the last section.
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Multi-parametric Le Roy function revisited Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-16 Sergei Rogosin, Maryna Dubatovskaya
This paper is a continuation of the recent article “Multi-parametric Le Roy function”, Fract. Calc. Appl. Anal. 26(5), 54–69 (2023), https://doi.org/10.1007/s13540-022-00119-y, by S. Rogosin and M. Dubatovskaya. Here we present further analytic properties of the Le Roy function depending on several parameters. Using the Mellin-Barnes representations we determine relations of the multi-parametric Le
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A bifurcation result for a Keller-Segel-type problem Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-16 Giovanni Molica Bisci, Raffaella Servadei, Luca Vilasi
We consider a parametric elliptic problem governed by the spectral Neumann fractional Laplacian on a bounded domain of \(\mathbb {R}^N\), \(N\ge 2\), with a general nonlinearity. This problem is related to the existence of steady states for Keller-Segel systems in which the diffusion of the chemical is nonlocal. By variational arguments we prove the existence of a weak solution as a local minimum of
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Nonlocal Kirchhoff-type problems with singular nonlinearity: existence, uniqueness and bifurcation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-07 Linlin Wang, Yuming Xing, Binlin Zhang
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On heat equations associated with fractional harmonic oscillators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-01 Divyang G. Bhimani, Ramesh Manna, Fabio Nicola, Sundaram Thangavelu, S. Ivan Trapasso
We establish some fixed-time decay estimates in Lebesgue spaces for the fractional heat propagator \(e^{-tH^{\beta }}\), \(t, \beta >0\), associated with the harmonic oscillator \(H=-\Delta + |x|^2\). We then prove some local and global wellposedness results for nonlinear fractional heat equations.
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Efficient spectral collocation method for fractional differential equation with Caputo-Hadamard derivative Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-31 Tinggang Zhao, Changpin Li, Dongxia Li
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Elastic metamaterials with fractional-order resonators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-31 Marcin B. Kaczmarek, S. Hassan HosseinNia
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Approximation results in Sobolev and fractional Sobolev spaces by sampling Kantorovich operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-01 Marco Cantarini, Danilo Costarelli, Gianluca Vinti
The present paper deals with the study of the approximation properties of the well-known sampling Kantorovich (SK) operators in “Sobolev-like settings”. More precisely, a convergence theorem in case of functions belonging to the usual Sobolev spaces for the SK operators has been established. In order to get such a result, suitable Strang-Fix type conditions have been required on the kernel functions
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Averaging principle for stochastic Caputo fractional differential equations with non-Lipschitz condition Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-11-03 Zhongkai Guo, Xiaoying Han, Junhao Hu
In this paper, the averaging principle for stochastic Caputo fractional differential equations (SCFDEs) with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence
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Spectral analysis of a family of nonsymmetric fractional elliptic operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-31 Quanling Deng, Yulong Li
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Approximation with continuous functions preserving fractal dimensions of the Riemann-Liouville operators of fractional calculus Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-30 Binyan Yu, Yongshun Liang
In this paper, we mainly make research on the approximation of continuous functions in the view of the fractal structure based on previous studies. Initially, fractal dimensions and the Hölder continuity of the linear combination of continuous functions have been explored and dense subsets of the space of continuous functions have also been studied. Then, it has been proved that the order of finding
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On the kinetics of $$\psi $$ -fractional differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-27 Weiyuan Ma, Changping Dai, Xin Li, Xionggai Bao
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Generalized fractional Dirac type operators Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-27 Joel E. Restrepo, Michael Ruzhansky, Durvudkhan Suragan
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional derivative and the fractional Laplacian, both operators defined with respect to some given functions. Direct and inverse fractional Cauchy type problems are studied for the introduced operators. We give explicit solutions of the considered fractional Cauchy
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Symmetry and monotonicity of positive solutions for Choquard equations involving a generalized tempered fractional p-Laplacian in $${\mathbb {R}}^{n}$$ Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-25 Linlin Fan, Linfen Cao, Peibiao Zhao
In this paper, we study a nonlinear system involving a generalized tempered fractional p-Laplacian in \({\mathbb {R}}^{n}\): $$\begin{aligned} \left\{ \begin{array}{ll} (-\varDelta -\lambda _{f})_{p}^{s}u(x)+\omega u(x)=C_{n,t}(|x|^{2t-n}*u^{q})u^{q-1}, &{}x\in {\mathbb {R}}^{n},\\ u(x)>0,&{}x\in {\mathbb {R}}^{n}, \end{array} \right. \end{aligned}$$ where \(02,\ p-10\). By using the direct method
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Well-posedness and regularity results for a class of fractional Langevin diffusion equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-13 Sen Wang, Xian-Feng Zhou, Wei Jiang, Denghao Pang
In the work presented in this paper, a study for a class of space-time fractional Langevin diffusion equations with two different time-fractional derivatives and a spatial fractional Laplacian was conducted. Firstly, we investigate the well-posedness and regularity of the mild solutions for a nonlocal problem by using several distinctly different approaches in the following three cases with the source
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Two-weighted estimates for p-adic Riesz potential and its commutators on Morrey–Herz spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-10 Ngo Thi Hong, Dao Van Duong
In this paper, we study the boundedness of p-adic Riesz potential on two-weighted Morrey–Herz spaces with both power weight and Muckenhoupt weight. Moreover, the boundedness for commutators of p-adic Riesz potential with symbols in Lipschitz spaces and weighted central BMO spaces on such spaces are also established.
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Association of a fractional order controller with an optimal model-based approach for a robust, safe and high performing control of nonlinear systems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-11 Evgeny Shulga, Patrick Lanusse, Tudor-Bogdan Airimitoaie, Stéphane Maurel
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Numerical investigation of generalized tempered-type integrodifferential equations with respect to another function Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-10-02 Wenlin Qiu, Omid Nikan, Zakieh Avazzadeh
This paper studies two efficient numerical methods for the generalized tempered integrodifferential equation with respect to another function. The proposed methods approximate the unknown solution through two phases. First, the backward Euler (BE) method and first-order interpolation quadrature rule are adopted to approximate the temporal derivative and generalized tempered integral term to construct
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A unified analysis framework for generalized fractional Moore–Gibson–Thompson equations: Well-posedness and singular limits Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-09-26 Mostafa Meliani
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Fractional models for analysis of economic risks Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-09-27 Sergei Rogosin, Maria Karpiyenya
In this review paper we try to describe some recent results on modeling and analysis of economic risks by using the techniques of fractional calculus. The use of fractional order operators in the risk theory is due to the presence of long and short memory in most of economic models and their nonlocality over time. We emphasize on the use and interpretation of the Dzherbashian-Caputo fractional derivative
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Method of separation of variables and exact solution of time fractional nonlinear partial differential and differential-difference equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-09-25 Chandrasekaran Uma Maheswari, Ramajayam Sahadevan, Munusamy Yogeshwaran
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Qualitative analysis of tripled system of fractional Langevin equations with cyclic anti-periodic boundary conditions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-09-19 Wei Zhang, Jinbo Ni
In this paper, we study the cyclic anti-periodic boundary value problem of a nonlinear tripled system of fractional Langevin equations. By means of Krasnoselskii fixed point theorem and Banach contraction mapping theorem, we obtain sufficient conditions for the existence and uniqueness of results. Moreover, we investigate the Ulam-Hyers and Ulam-Hyers-Rassias stabilities of the proposed problem. Finally
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Properties of the multi-index special function $${\mathcal {W}}^{\left( \bar{\alpha },\bar{\nu }\right) }(z)$$ Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-09-05 Riccardo Droghei
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Homogenization and inverse problems for fractional diffusion equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-29 Atsushi Kawamoto, Manabu Machida, Masahiro Yamamoto
We consider the homogenization for time-fractional diffusion equations in a periodic structure. First, we derive the homogenized time-fractional diffusion equations. Next, we prove the stability in determining a constant diffusion coefficient by minimum data. Moreover, we investigate the inverse problems of estimating the homogenized diffusion coefficient by the data for non-homogenized structure.
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A variational theory for integral functionals involving finite-horizon fractional gradients Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-28 Javier Cueto, Carolin Kreisbeck, Hidde Schönberger
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Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-18 Yiqun Li, Hong Wang, Xiangcheng Zheng
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Existence results for singular elliptic problem involving a fractional p-Laplacian Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-18 Hanaâ Achour, Sabri Bensid
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Fractional integral operator and its commutator on generalized Morrey spaces associated with ball Banach function spaces Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-14 Mingquan Wei
In this paper, we study the boundedness for the fractional integral operator \(I_\alpha \) on generalized Morrey spaces associated with ball Banach function spaces. Moreover, the boundeness for the commutator of \(I_\alpha \) on these spaces is also established. Our main results extend various previous results on some concrete generalized Morrey spaces associated with ball Banach function spaces.
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An elementary inequality for dissipative Caputo fractional differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-14 Peter E. Kloeden
An elementary inequality is discussed for autonomous Caputo fractional differential equation (FDE) of order \(\alpha \in (0,1)\) in \(\mathbb {R}^d\) for which the vector field satisfies a dissipativity condition. This inequality is fundamental for investigating qualitative and dynamical properties of such equations. Here its use and effectiveness are illustrated to show the global existence and uniqueness
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Uncertainty principles of hypercomplex functions for fractional Fourier transform Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-11 Wen-Biao Gao
In the present paper, different uncertainty principles for hypercomplex functions associated with the fractional Fourier transform (FRFT) are investigated. First, the inverse formula and Plancherel theorem of the FRFT are obtained. Then, a new uncertainty principle for the FRFT of hypercomplex functions in the time and FRFT domains is explored. Moreover, an uncertainty principle in two FRFT domains
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Mellin definition of the fractional Laplacian Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-04 Gianni Pagnini, Claudio Runfola
It is known that at least ten equivalent definitions of the fractional Laplacian exist in an unbounded domain. Here we derive a further equivalent definition that is based on the Mellin transform and it can be used when the fractional Laplacian is applied to radial functions. The main finding is tested in the case of the space-fractional diffusion equation. The one-dimensional case is also considered
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Classical versus fractional difference equations: the logistic case Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-08-01 Jose S. Cánovas
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Global attractivity for fractional differential equations of Riemann-Liouville type Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-21 Tao Zhu
By the Schauder fixed point theorem and generalized Ascoli-Arzela theorem, we present that the Riemann-Liouville fractional differential equation has at least one globally attractive solution and \(x(t)=x_{0}t^{\beta -1}+o(t^{\beta -\gamma _{1}})\) as \(t\rightarrow +\infty \), where \(\beta<\gamma _{1}<\gamma <1\). The novelty in this paper is that the global solution of Riemann-Liouville fractional
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High order approximations of solutions to initial value problems for linear fractional integro-differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-17 Neville J. Ford, Arvet Pedas, Mikk Vikerpuur
We consider a general class of linear integro-differential equations with Caputo fractional derivatives and weakly singular kernels. First, the underlying initial value problem is reformulated as an integral equation and the possible singular behavior of its exact solution is determined. After that, using a suitable smoothing transformation and spline collocation techniques, the numerical solution
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On approximate controllability of semi-linear neutral integro-differential evolution systems with state-dependent nonlocal conditions Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-17 Nan Cao, Xianlong Fu
This paper is concerned with the approximate controllability of a class of semi-linear neutral integro-differential equation with nonlocal condition. The basic tools of this study are the theory of resolvent operators of linear neutral integro-differential equation and fractional powers. The fundamental solution of linear neutral integro-differential equations is also constructed to deal with the non-uniform
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A new approach to multi-delay matrix valued fractional linear differential equations with constant coefficients Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-10 Antônio Francisco Neto
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On the Rothe-Galerkin spectral discretization for a class of variable fractional-order nonlinear wave equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-06 Karel Van Bockstal, Mahmoud A. Zaky, Ahmed Hendy
In this contribution, a wave equation with a time-dependent variable-order fractional damping term and a nonlinear source is considered. Avoiding the circumstances of expressing the nonlinear variable-order fractional wave equations via closed-form expressions in terms of special functions, we investigate the existence and uniqueness of this problem with Rothe’s method. First, the weak formulation
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Inverse problem of determining the order of the fractional derivative in the Rayleigh-Stokes equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-06 Ravshan Ashurov, Oqila Mukhiddinova
In recent years, much attention has been paid to the study of forward and inverse problems for the Rayleigh-Stokes equation in connection with the importance of this equation for applications. This equation plays an important role, in particular, in the study of the behavior of certain non-Newtonian fluids. The equation includes a fractional derivative of order \(\alpha \), which is used to describe
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An ADMM approach to a TV model for identifying two coefficients in the time-fractional diffusion system Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-06 Mohemmad Srati, Abdessamad Oulmelk, Lekbir Afraites, Aissam Hadri
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Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part I: Linear equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-07-06 Yuri Luchko, Masahiro Yamamoto
The main objective of this paper is analysis of the initial-boundary value problems for the linear time-fractional diffusion equations with a uniformly elliptic spatial differential operator of the second order and the Caputo type time-fractional derivative acting in the fractional Sobolev spaces. The boundary conditions are formulated in form of the homogeneous Neumann or Robin conditions. First we
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Multiplicity of solutions for a fractional Kirchhoff type equation with a critical nonlocal term Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-29 Xilin Dou, Xiaoming He
This paper is concerned with the multiplicity of solutions for the fractional Kirchhoff type equations with a critical nonlocal term $$\begin{aligned} {\left\{ \begin{array}{ll}\displaystyle M\left( \Vert u\Vert ^2_Z\right) \mathscr {L}_K u=\lambda f(x,u)+ \left( \int _{\varOmega }\frac{|u(y)|^{2^*_{\alpha ,s}}}{|x-y|^{\alpha }}dy\right) |u|^{2^*_{\alpha ,s}-2}u,&{} x\in \varOmega , \\ u(x)=0, &{}x\in
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Global existence and finite time blowup for a fractional pseudo-parabolic p-Laplacian equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-26 Jiazhuo Cheng, Qiru Wang
In this paper, we study the initial-boundary value problem for a fractional pseudo-parabolic p-Laplacian type equation. First, by means of the imbedding theorems, the theory of potential wells and the Galerkin method, we prove the existence and uniqueness of global solutions with subcritical initial energy, critical initial energy and supercritical initial energy, respectively. Next, we establish the
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Existence and uniqueness of a weak solution to fractional single-phase-lag heat equation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-19 Frederick Maes, Karel Van Bockstal
In this article, we study the existence and uniqueness of a weak solution to the fractional single-phase lag heat equation. This model contains the terms \(\mathcal {D}_t^\alpha (\partial _{t}u)\) and \(\mathcal {D}_t^\alpha u \) (with \(\alpha \in (0,1)\)), where \(\mathcal {D}_t^\alpha \) denotes the Caputo fractional differential operator (in time) of order \(\alpha \). We consider homogeneous Dirichlet
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Solvability of an infinite system of Langevin fractional differential equations in a new tempered sequence space Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-16 Inzamamul Haque, Javid Ali, M. Mursaleen
In this article, we establish a new tempered sequence space related to tempered sequence \(\ell _{p}^{\alpha },\) \(p\ge 1\) and obtain the Hausdorff measure of noncompactness of this space. By using this measure of noncompactness with Darbo’s fixed point theorem, we investigate the existence results for an infinite system of Langevin fractional differential equations involving a generalized derivative
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Fourth-order cumulants based-least squares methods for fractional Multiple-Input-Single-Output Errors-In-Variables system identification Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-16 Manel Chetoui, Mohamed Aoun
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The Lambert function method in qualitative analysis of fractional delay differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-16 Jan Čermák, Tomáš Kisela, Luděk Nechvátal
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Two families of second-order fractional numerical formulas and applications to fractional differential equations Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-06 Baoli Yin, Yang Liu, Hong Li, Zhimin Zhang
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Controllability and observability of linear time-varying fractional systems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-05 Maja Jolić, Sanja Konjik
We consider linear time-varying control problems involving the Caputo fractional derivative. By introducing the controllability Gramian matrix, we prove that the invertibility of the Gramian is a necessary and sufficient condition for controllability. Furthermore, we prove equivalence between controllability and observability of the associated adjoint problem. Using methods from linear control theory
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Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-06-05 Tong Zhang, Jie-Xiang Zhu
We establish a novel definition of the fractional gradient and divergence of order \(\alpha \in (0, 1)\) through the use of Riesz potential on homogeneous Carnot groups. We introduce and investigate the distributional fractional Sobolev space and the space of fractional BV functions in this context. Additionally, we provide a definition of fractional Caccioppoli sets on homogeneous Carnot groups and
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An inverse problem of determining the fractional order in the TFDE using the measurement at one space-time point Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-31 Gongsheng Li, Zhen Wang, Xianzheng Jia, Yi Zhang
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Optimal approximation of analog PID controllers of complex fractional-order Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-30 Shibendu Mahata, Norbert Herencsar, Guido Maione
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Small order limit of fractional Dirichlet sublinear-type problems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-24 Felipe Angeles, Alberto Saldaña
We study the asymptotic behavior of solutions to various Dirichlet sublinear-type problems involving the fractional Laplacian when the fractional parameter s tends to zero. Depending on the type on nonlinearity, positive solutions may converge to a characteristic function or to a positive solution of a limit nonlinear problem in terms of the logarithmic Laplacian, that is, the pseudodifferential operator
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Wind turbulence modeling for real-time simulation Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-22 Mohamed Hajjem, Stéphane Victor, Pierre Melchior, Patrick Lanusse, Lara Thomas
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Queuing models with Mittag-Leffler inter-event times Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-18 Jacob Butt, Nicos Georgiou, Enrico Scalas
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Approximate controllability results for the Sobolev type fractional delay impulsive integrodifferential inclusions of order $${r} \in (1,2)$$ via sectorial operator Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-15 M. Mohan Raja, V. Vijayakumar
In this study, we investigate nonlocal problems for a class of the Sobolev type fractional delay impulsive integrodifferential inclusions of order \({r} \in (1,2)\) via sectorial operator in Hilbert space. The results are obtained by engaging of mixed Volterra-Fredholm integrodifferential systems, sectorial operator of type \((P,\kappa ,{r},\gamma )\) and Martelli’s fixed point theorem under the assumption
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Sharp error estimates for spatial-temporal finite difference approximations to fractional sub-diffusion equation without regularity assumption on the exact solution Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-11 Daxin Nie, Jing Sun, Weihua Deng
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Game-theoretical problems for fractional-order nonstationary systems Fract. Calc. Appl. Anal. (IF 3.0) Pub Date : 2023-05-10 Ivan Matychyn, Viktoriia Onyshchenko
Nonstationary fractional-order systems represent a new class of dynamic systems characterized by time-varying parameters as well as memory effect and hereditary properties. Differential game described by system of linear nonstationary differential equations of fractional order is treated in the paper. The game involves two players, one of which tries to bring the system’s trajectory to a terminal set