Fractional calculus is at this stage an arena where many models are still to be introduced,
discussed and applied to real world applications in many branches of science and …

Dynamics in fractional order systems has been discussed extensively for presenting a
possible guidance in the field of applied mathematics and interdisciplinary science. Within …

New variable-order fractional chaotic systems are proposed in this paper. A concept of short
memory is introduced where the initial point in the Caputo derivative is varied. The fractional …

A new fractional order Gronwall inequality with time delay is developed in this paper. Based
on this inequality, a new criterion for finite-time synchronization of fractional order memristor …

In this article, the finite-time stability (FTS) of fractional-order Hopfield neural networks with
time delays (FHNNTDs) is studied. A widely used inequality in investigating the stability of …

In the present study, we explore the topological classifications at fixed points, global
dynamics, Neimark-Sacker bifurcation and hybrid control in the two-dimensional discrete …

This paper is concerned with numerical solutions of nonlinear time fractional reaction–
diffusion equations with time delay. A linearized compact finite difference scheme is …

Variable-order fractional discrete calculus is a new and unexplored part of calculus that
provides extraordinary capabilities for simulating multidisciplinary processes. Recognizing …

In this article, we discuss the existence and uniqueness of solution of a delay Caputo q-
fractional difference system. Based on the q-fractional Gronwall inequality, we analyze the …

We revisit motivation of the fractional difference equations and some recent applications to
image encryption. Then stability of impulsive fractional difference equations is investigated …