相关论文: On the analysis of mixed-index time fractional dif…

The Laplace transform method for solving of a wide class of initial value problems for fractional differential equations is introduced. The method is based on the Laplace transform of the Mittag-Leffler function in two parameters. To extend…

We introduce the delayed Mittag-Leffler type matrix functions, delayed fractional cosine, delayed fractional sine and use the Laplace transform to obtain an analytical solution to the IVP for a Hilfer type fractional linear time-delay…

A recent development in the theory of fractional differential equations with variable coefficients has been a method for obtaining an exact solution in the form of an infinite series involving nested fractional integral operators. This…

This paper is devoted to the general theory of systems of time-fractional differential-operator equations. The representation formulas for solutions of systems of ordinary differential equations with single (commensurate) fractional order…

In this paper we investigate the solution of generalized distributed order diffusion equations with composite time fractional derivative by using the Fourier-Laplace transform method. We represent solutions in terms of infinite series in…

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…

It is well-known that one-dimensional time fractional diffusion-wave equations with variable coefficients can be reduced to ordinary fractional differential equations and systems of linear fractional differential equations via scaling…

We introduce new fractional operators of variable order on isolated time scales with Mittag-Leffler kernels. This allows a general formulation of a class of fractional variational problems involving variable-order difference operators. Main…

In this paper, we introduce a delayed Mittag-Leffler type function. With the help of the delayed Mittag-Leffler type functions, we give an explicit formula of solutions to linear nonhomogeneous fractional time-delay Langevin equations…

This paper investigates an inverse source problem for a multi-term time-fractional diffusion equation with Caputo derivatives. The source term is separable as \(f(x)g(t)\), with the unknown spatial component \(f(x)\) reconstructed from an…

In this paper, the invariant subspace method is applied to the time fractional modified Kuramoto-Sivashinsky partial differential equation. The obtained reduced system of nonlinear ordinary fractional equations is solved by the Laplace…

This paper is devoted to the investigation of the backward problem for a multi-term time-fractional diffusion equation. Backward problems for fractional diffusion equations are typically studied using regularization methods due to their…

In this paper, we propose a delayed perturbation of Mittag-Leffler type matrix function, which is an extension of the classical Mittag-Leffler type matrix function and delayed Mittag-Leffler type matrix function. With the help of the…

In this paper we study some cases of time-fractional nonlinear dispersive equations (NDEs) involving Caputo derivatives, by means of the invariant subspace method. This method allows to find exact solutions to nonlinear time-fractional…

In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…

This paper introduces a generalized fractional Halanay-type coupled inequality, which serves as a robust tool for characterizing the asymptotic stability of diverse time fractional functional differential equations, particularly those…

In this paper, we study a class of multi-order fractional nonlinear delay systems. Our main contribution is to show the (local or global) Mittag-Leffler stability of systems when some structural assumptions are imposed on the "vector…

We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown…

We propose a delayed Mittag-Leffler type matrix function with logarithm, which is an extension of the classical Mittag-Leffler type matrix function with logarithm and delayed Mittag-Leffler type matrix function. With the help of the delayed…

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate partial differential equation and the second one…