An outlook on stability of implicit \(\theta\)-Caputo fractional differential equation with application involving the Riemann-Stieltjes type

Volume 34, Issue 1, pp 35--51 https://dx.doi.org/10.22436/jmcs.034.01.04

Publication Date: February 14, 2024 Submission Date: September 04, 2023 Revision Date: December 06, 2023 Accteptance Date: January 03, 2024

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Authors

A. M. A. El-Sayed - Faculty of Sciences, Department of Mathematics, Alexandria University, Alexandria, Egypt. Sh. M. Al-Issa - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon. - Faculty of Arts and Sciences, Department of Mathematics, International University of Beirut, Beirut, Lebanon. I. H. Kaddoura - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon. - Faculty of Arts and Sciences, Department of Mathematics, The International University of Beirut, Beirut, Lebanon. Z. A. Sleiman - Faculty of Arts and Sciences, Department of Mathematics , Lebanese International University, Saida, Lebanon.

Abstract

The objective of the current article is to guarantee the solvability of implicit \(\theta\)-Caputo fractional differential equations with integral boundary conditions. We establish the necessary conditions to guarantee unique solutions and demonstrate Ulam-Hyers-Rassias stability. Additionally, we include examples to illustrate the key findings.

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Keywords

• \(\theta\)-Caputo fractional operator
• mild solution
• Ulam stability
• Riemann-Stieltjes

MSC

•  26A33
•  34A60
•  45G05

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