Qualitative Analyses of Fractional Integrodifferential Equations with a Variable Order under the Mittag-Leffler Power Law. (20th April 2022)

• Record Type: Journal Article
• Authors: Jeelani, Mdi Begum; Alnahdi, Abeer S.; Almalahi, Mohammed A.; Abdo, Mohammed S.; Wahash, Hanan A.; Alharthi, Nadiyah Hussain
• Other Names: An Tianqing Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2022(2022)
• Publication Date: 2022-04-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2022/6387351
• Languages: English
• ISSNs: 2314-8896

Abstract

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.