Caputo-Katugampola-type implicit fractional differential equation with anti-periodic boundary conditions

Year 2022, Volume: 5 Issue: 1, 12 - 28, 31.03.2022

Saleh Redhwan , Sadikali Shaikh , Mohammed Abdo

https://doi.org/10.53006/rna.974148

Cited By: 5

Abstract

The given article describes the implicit fractional dierential equation with anti-periodic boundary conditions
in the frame of Caputo-Katugampola fractional derivative. We obtain an analogous integral equation of the
given problem and prove the existence and uniqueness results of such a problem using the Banach and
Krasnoselskii xed point theorems. Further, by applying generalized Gronwall inequality, the Ulam-Hyers
stability results are discussed. To show the eectiveness of the acquired results, convenient examples are
presented.

Keywords

implicit fractional differential equation, fractional derivative and fractional integral, anti-periodic conditions, fixed point theorem, Gronwall inequality

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