On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

Usman Riaz, Akbar Zada, Zeeshan Ali, Ioan-Lucian Popa, Shahram Rezapour and Sina Etemad
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Usman Riaz: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
Akbar Zada: Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
Zeeshan Ali: School of Engineering, Monash University Malaysia, Selangor 47500, Malaysia
Ioan-Lucian Popa: Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, Alba Iulia 510009, Romania
Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran

Mathematics, 2021, vol. 9, issue 11, 1-22

Abstract: We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.

Keywords: Riemann–Liouville fractional derivative; coupled system; fractional order boundary conditions; green function; existence theory; Ulam stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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