On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique

Ahmed Refice,Ivanka Stamova,Mohammed Said Souid

doi:10.3390/math9101134

Abstract

In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of the observed results.

Highlights

Order via Kuratowski MNCThe idea of fractional calculus is to replace the natural numbers in the derivative’s order with rational ones
It is often difficult to find the analytical solution of fractional differential equations (FDEqs) of variable order; numerical methods for the approximation of
We contribute to the development of the existence theory of boundary value problems with variable-order Hadamard derivatives

Summary

Introduction

The idea of fractional calculus is to replace the natural numbers in the derivative’s order with rational ones It seems an elementary consideration, it has an exciting correspondence explaining some physical phenomena. A recent improvement in this investigation is the consideration of the notion of variable order operators In this sense, various definitions of fractional operators involving the variable order have been introduced. Various definitions of fractional operators involving the variable order have been introduced This type of operators which are dependent on their power-law kernel can describe some hereditary specifications of numerous processes and phenomena [19,20]. In [29], Zhuang et al introduced the implicit and explicit Euler approximations for the nonlinear diffusion-advection equation of variable order

Objectives

Results

Conclusion