On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions †
1
Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25000, Pakistan
2
School of Engineering, Monash University Malaysia, Selangor 47500, Malaysia
3
Department of Computing, Mathematics and Electronics, “1 Decembrie 1918” University of Alba Iulia, Alba Iulia 510009, Romania
4
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 51368, Iran
5
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 404, Taiwan
*
Authors to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Academic Editor: Ioannis Dassios
Mathematics 2021, 9(11), 1205; https://doi.org/10.3390/math9111205
Received: 16 April 2021
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Revised: 19 May 2021
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Accepted: 24 May 2021
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Published: 26 May 2021
(This article belongs to the Special Issue Dynamical Systems in Engineering)
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.
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Keywords:
Riemann–Liouville fractional derivative; coupled system; fractional order boundary conditions; green function; existence theory; Ulam stability
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MDPI and ACS Style
Riaz, U.; Zada, A.; Ali, Z.; Popa, I.-L.; Rezapour, S.; Etemad, S. On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions. Mathematics 2021, 9, 1205. https://doi.org/10.3390/math9111205
AMA Style
Riaz U, Zada A, Ali Z, Popa I-L, Rezapour S, Etemad S. On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions. Mathematics. 2021; 9(11):1205. https://doi.org/10.3390/math9111205
Chicago/Turabian StyleRiaz, Usman, Akbar Zada, Zeeshan Ali, Ioan-Lucian Popa, Shahram Rezapour, and Sina Etemad. 2021. "On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions" Mathematics 9, no. 11: 1205. https://doi.org/10.3390/math9111205
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