AIMS Mathematics (Feb 2022)

On a novel impulsive boundary value pantograph problem under Caputo proportional fractional derivative operator with respect to another function

  • Songkran Pleumpreedaporn,
  • Chanidaporn Pleumpreedaporn,
  • Weerawat Sudsutad ,
  • Jutarat Kongson,
  • Chatthai Thaiprayoon ,
  • Jehad Alzabut

DOI
https://doi.org/10.3934/math.2022438
Journal volume & issue
Vol. 7, no. 5
pp. 7817 – 7846

Abstract

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In this manuscript, we study the existence and Ulam's stability results for impulsive multi-order Caputo proportional fractional pantograph differential equations equipped with boundary and integral conditions with respect to another function. The uniqueness result is proved via Banach's fixed point theorem, and the existence results are based on Schaefer's fixed point theorem. In addition, the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the proposed problem are obtained by applying the nonlinear functional analysis technique. Finally, numerical examples are provided to supplement the applicability of the acquired theoretical results.

Keywords