Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law

Author:

Jeelani Mdi Begum1ORCID,Alnahdi Abeer S.1ORCID,Almalahi Mohammed A.2ORCID,Abdo Mohammed S.3ORCID,Wahash Hanan A.4ORCID,Alharthi Nadiyah Hussain1ORCID

Affiliation:

1. Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 13314, Saudi Arabia

2. Department of Mathematics, Hajjah University, Hajjah, Yemen

3. Department of Mathematics, Hodeidah University, Al-Hudaydah, Yemen

4. Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, M.S 431001, India

Abstract

This research paper intends to study some qualitative analyses for a nonlinear fractional integrodifferential equation with a variable order in the frame of a Mittag-Leffler power law. At first, we convert the considered problem of variable order into an equivalent standard problem of constant order using generalized intervals and piecewise constant functions. Next, we prove the existence and uniqueness of analytic results by application of Krasnoselskii’s and Banach’s fixed point theorems. Besides, the guarantee of the existence of solutions is shown by different types of Ulam-Hyer’s stability. Then, we investigate sufficient conditions of positive solutions for the proposed problem. In the end, we discuss an example to illustrate the applicability of our obtained results.

Funder

Imam Mohammad Ibn Saud Islamic University

Publisher

Hindawi Limited

Subject

Analysis

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