ANALYTICAL TREATMENTS TO SYSTEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH MODIFIED ATANGANA–BALEANU DERIVATIVE

Mohammed Al-Refai (), Muhammed I. Syam and Dumitru Baleanu
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Mohammed Al-Refai: Department of Mathematics, College of Science, Yarmouk University, Irbid 21163, Jordan
Muhammed I. Syam: Department of Mathematical Sciences, UAE University, Sheik Khalifa Bin Zayed St, Asharij Abu Dhabi, Al Ain, UAE
Dumitru Baleanu: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon4Department of Mathematics, Cankaya University, Ankara, Turkey5Institute of Space Sciences, Magurele-Bucharest, Romania

FRACTALS (fractals), 2023, vol. 31, issue 10, 1-12

Abstract: The solutions of systems of fractional differential equations depend on the type of the fractional derivative used in the system. In this paper, we present in closed forms the solutions of linear systems involving the modified Atangana–Baleanu derivative that has been introduced recently. For the nonlinear systems, we implement a numerical scheme based on the collocation method to obtain approximate solutions. The applicability of the results is tested through several examples. We emphasize here that certain systems with the Atangana–Baleanu derivative admit no solutions which is not the case with the modified derivative.

Keywords: Fractional Differential Equations; Linear Systems; Mittag-Leffler Kernel (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23401564

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