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QUALITATIVE STUDY OF NONLINEAR COUPLED PANTOGRAPH DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

ISRAR AHAMAD

Department of Mathematics, University of Malakand, Chakdara Dir (lower), Khyber Pakhtunkhawa, Pakistan

E-mail Address: israrahmadjc503@gmail.com

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KAMAL SHAH

Department of Mathematics, University of Malakand, Chakdara Dir (lower), Khyber Pakhtunkhawa, Pakistan

E-mail Address: kamalshah408@gmail.com

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THABET ABDELJAWAD

Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia

Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan

E-mail Address: tabdeljawad@psu.edu.sa

Corresponding author.

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, and

FAHD JARAD

Department of Mathematics, Çankaya University, Ankara 06790, Turkey

E-mail Address: fahd@cankaya.edu.tr

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https://doi.org/10.1142/S0218348X20400459Cited by:6 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this paper, we investigate a nonlinear coupled system of fractional pantograph differential equations (FPDEs). The respective results address some adequate results for existence and uniqueness of solution to the problem under consideration. In light of fixed point theorems like Banach and Krasnoselskii’s, we establish the required results. Considering the tools of nonlinear analysis, we develop some results regarding Ulam–Hyers (UH) stability. We give three pertinent examples to demonstrate our main work.

Keywords:

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Vol. 28, No. 08

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History

Received 16 December 2019

Accepted 6 February 2020

Published: September 18, 2020

Information

This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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QUALITATIVE STUDY OF NONLINEAR COUPLED PANTOGRAPH DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER

Abstract

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