Existence and $\delta $-Approximate solution of implicit fractional pantograph equations in the frame of Hilfer-Katugampola operator

https://doi.org/10.48185/jfcns.v2i1.59

Authors

  • Mohammed A. Almalahi Dr. Babasaheb Ambedkar Marathwada University
  • Satish. K Panchal Dr. Babasaheb Ambedkar Marathwada University

Keywords:

Hilfer-Katugampola fractional derivative, Existence, Nonlocal conditions, $\delta $ -approximate solution

Abstract

The major goal of this research paper is to investigate the existence and uniqueness of an implicit fractional pantograph equation in the frame of the Hilfer-Katugampola operator on the finite interval $[a,b]$ with mixed nonlocal conditions. Our analysis of the existence and uniqueness of solutions depends on some fixed point theorems such as Banach and Krasnoselskii. Moreover, we discuss the dependence of solutions on mixed nonlocal conditions by means of $\delta $-approximated solution. As an application, we provide an example to illustrate the validity of our results.

Published

2021-06-29

How to Cite

Almalahi, M. A., & Panchal, S. K. (2021). Existence and $\delta $-Approximate solution of implicit fractional pantograph equations in the frame of Hilfer-Katugampola operator. Journal of Fractional Calculus and Nonlinear Systems, 2(1), 1–17. https://doi.org/10.48185/jfcns.v2i1.59