On the qualitative analysis of the boundary value problem of the Ψ-Caputo implicit fractional pantograph differential equation

Rahman Ullah  Khan; Maria  Samreen; Gohar  Ali; Ioannis  Argyros

doi:10.59400/jam1977

On the qualitative analysis of the boundary value problem of the Ψ-Caputo implicit fractional pantograph differential equation

Rahman Ullah Khan Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Maria Samreen Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Gohar Ali Department of Mathematics, Islamia College Peshawar, Peshawar 25120, Pakistan
Ioannis Argyros Department of Computing and Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

Article ID: 1977

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DOI: https://doi.org/10.59400/jam1977

Keywords: fractional differential equation; Ψ-Caputo fractional derivative; fixed point results; stability

Abstract

In this manuscript, the primary objective is to analyze a Ψ-Caputo fractional pantograph implicit differential equation using the Ψ-Caputo fractional derivative. We employ a newly developed method based on fixed-point theorems to explore the existence and uniqueness of the solution to our proposed problem. Furthermore, we investigate the stability of the proposed problem. Finally, we provide an example that illustrates the application of our newly obtained results, confirming their practical significance.

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Published

2024-11-30

How to Cite

Khan, R. U., Samreen, M., Ali, G., & Argyros, I. (2024). On the qualitative analysis of the boundary value problem of the Ψ-Caputo implicit fractional pantograph differential equation. Journal of AppliedMath, 2(6), 1977. https://doi.org/10.59400/jam1977

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