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In the present work, we investigate a uniqueness of solution of the inverse source problem with non-local conditions for mixed parabolic-hyperbolic type equation with Caputo fractional derivative. Solution of the problem we represent as…
We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under…
In this paper, the fractional differential matrices based on the Jacobi-Gauss points are derived with respect to the Caputo and Riemann-Liouville fractional derivative operators. The spectral radii of the fractional differential matrices…
We study three types of generalized partial fractional operators. An extension of Green's theorem, by considering partial fractional derivatives with more general kernels, is proved. New results are obtained, even in the particular case…
A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a couple of spatially second-order system and we use an…
In this paper, we study some new properties of Sadik transform such as integration, time delay, initial value theorem, and final value theorem. Moreover, we prove the theorem of Sadik transform for Caputo fractional derivative and we also…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Almost nothing is known about the layer structure of solutions to singularly perturbed Caputo fractional boundary value problems. We discuss simple convection-diffusion and reaction-diffusion problems.
We discuss the existence of stationary solutions for logistic diffusion equations of Fisher-Kolmogoroff-Petrovski-Piskunov type driven by the superposition of fractional operators in a bounded region with "hostile" environmental conditions,…
It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sense that a unique solution exists and that this solution…
In this paper we establish some convergence results for Riemann-Liouville, Caputo, and Caputo-Fabrizio fractional operators when the order of differentiation approaches one. We consider some errors given by $\left|\left| D^{1-\al}f…
We prove continuity properties of higher order commutators of fractional operators on the multilinear setting, between a product of weighted Lebesgue spaces into certain weighted Lipschitz spaces. The considered operators include the…
Different fractional difference types of Euler-Lagrange equations are obtained within Riemann and Caputo by making use of different versions of integration by part forumlas in fractional difference calculus. An example is presented to…
In recent years, the use of variable-order differential operators has emerged as a powerful tool in the analysis of nonlinear fractional differential equations and chaotic systems. In finance, the accurate prediction of market trends and…
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…
The transformation property of the Caputo fractional derivative operator of a scalar function under rotation in two dimensional space is derived. The study of the transformation property is essential for the formulation of fractional…
We establish trace and extension theorems for evolutionary equations with the Caputo fractional derivatives in (weighted) $L_p$ spaces. To achieve this, we identify weighted Sobolev and Besov spaces with mixed norms that accommodate…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport…