Existence and Hyers-Ulam stability of solutions to the implicit second-order differential equation via fractional integral boundary conditions

Volume 31, Issue 1, pp 15--29 http://dx.doi.org/10.22436/jmcs.031.01.02

Publication Date: April 04, 2023 Submission Date: July 06, 2022 Revision Date: December 31, 2022 Accteptance Date: February 07, 2023

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Authors

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, The 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. N. J. Rifai - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon.

Abstract

In this paper, the existence and Ulam-Hyers stability of solutions for implicit second order fractional differential equations are investigated via fractional-orders integral boundary conditions. Our results are based on Krasnoselskii's fixed point Theorem and Banach contraction principle. We provide examples at the end to clarify our acquired outcomes..

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Keywords

• \(\phi\)-Caputo fractional order
• existence results
• Green's function
• boundary value problems
• Ulam-Hyers stability

MSC

•  26A33
•  34A60
•  45G05

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