Qualitative Study on \(\psi-\)Caputo fractional differential inclusion with non-local conditions and feedback control

Volume 34, Issue 3, pp 295--312 https://dx.doi.org/10.22436/jmcs.034.03.08

Publication Date: April 02, 2024 Submission Date: September 10, 2023 Revision Date: February 20, 2024 Accteptance Date: February 27, 2024

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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, Alexandria, Beirut, Lebanon. A. M. A. El-Sayed - Faculty of Sciences, Department of Mathematics, Alexandria University, Alexandria, Egypt. 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. F. H. Sheet - Faculty of Arts and Sciences, Department of Mathematics, Lebanese International University, Saida, Lebanon.

Abstract

This article discuss the existence of solutions for certain classes of nonlinear \(\psi\)–Caputo fractional derivative differential inclusion via a nonlocal infinite-point or Riemann–Stieltjes integral boundary conditions and with a feedback control in Banach spaces. Our approach is based on Schauder's fixed point theorem. We establish appropriate conditions that guarantee unique solutions and demonstrate that the solution continuously depends on the set of selections and some other functions. Additionally, we include {example} to illustrate the key findings.

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Keywords

• \(\psi\)-Caputo fractional operator
• Riemann-Stieltjes integral boundary conditions
• infinite-point boundary conditions
• feedback control

MSC

•  26A33
•  34A60
•  45G05

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