Related papers: Discrete delayed perturbation of Mittag-Leffler fu…
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…
The purpose of this article is to introduce the original results which devoted with the nonlinear control system problems involves of nonlinear differential equations of fractional orders. Thus, this system is described with a mixed of…
This paper focuses on the study of integro-differential equations with delays, presenting a novel perturbation approach. The primary objective is to introduce the concepts of classical and mild solutions for these equations and establish…
This paper investigates the time--domain response of nabla discrete fractional order systems by exploring several useful properties of the nabla discrete Laplace transform and the discrete Mittag--Leffler function. In particular, we…
Our aim in this paper is to investigate the asymptotic behavior of solutions of the perturbed linear fractional differential system. We show that if the original linear autonomous system is asymptotically stable then under the action of…
In this paper, we reformulate certain nabla fractional difference equations which had been investigated by other researchers. The previous results seem to be incomplete. By using Contraction Mapping Theorem, we establish conditions under…
We propose a new monotone finite difference discretization for the variational $p$-Laplace operator, \[ \Delta_p u=\text{div}(|\nabla u|^{p-2}\nabla u), \] and present a convergent numerical scheme for related Dirichlet problems. The…
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…
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…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
Explicit solutions of differential equations of complex fractional orders with respect to functions and with continuous variable coefficients are established. The representations of solutions are given in terms of some convergent infinite…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
We examine a fractional Discrete Nonlinear Schrodinger dimer, where the usual first-order derivative of the time evolution is replaced by a non integer-order derivative. The dimer is nonlinear (Kerr) and PT -symmetric, and we examine the…
In this paper we introduce a novel Mittag--Leffler-type function and study its properties in relation to some integro-differential operators involving Hadamard fractional derivatives or Hyper-Bessel-type operators. We discuss then the…
This work establishes a comprehensive analytical framework for studying implicit fractional differential systems with distributed memory and time delays. We develop novel fractional integral inequalities of Gr\"onwall--Wendroff type that…
This paper deals with the gradient stability and the gradient stabilizability of Caputo time fractional diffusion linear systems. First, we give sufficient conditions that allow the gradient Mittag-Leffler and strong stability, where we use…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
This paper deals with initial value problems for fractional functional differential equations with bounded delay. The fractional derivative is defined in the Caputo sense. By using the Schauder fixed point theorem and the properties of the…
In this work we prove the existence of solution for a class of perturbed fractional Hamiltonian systems given by \begin{eqnarray}\label{eq00} -{_{t}}D_{\infty}^{\alpha}(_{-\infty}D_{t}^{\alpha}u(t)) - L(t)u(t) + \nabla W(t,u(t)) = f(t),…