Involvement of the fixed point technique for solving a fractional differential system

Hasanen A. Hammad; Manuel De la Sen; Hasanen A. Hammad; Manuel De la Sen

doi:10.3934/math.2022395

AIMS Mathematics

2022, Volume 7, Issue 4: 7093-7105. doi: 10.3934/math.2022395

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Involvement of the fixed point technique for solving a fractional differential system

Hasanen A. Hammad ^{1
,
,},
Manuel De la Sen ²

1.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
2.
Institute of Research and Development of Processes, University of the Basque Country, 48940 Leioa (Bizkaia), Spain

Received: 23 December 2021 Revised: 21 January 2022 Accepted: 26 January 2022 Published: 08 February 2022
MSC : 34A08, 34A12, 34B15, 47H10

Some physical phenomena were described through fractional differential equations and compared with integer-order differential equations which have better results, which is why researchers of different areas have paid great attention to study this direction. So, in this manuscript, we discuss the existence and uniqueness of solutions to a system of fractional deferential equations (FDEs) under Riemann-Liouville (R-L) integral boundary conditions. The solution method is obtained by two basic rules, the first rule is the Leray-Schauder alternative and the second is the Banach contraction principle. Finally, the theoretical results are supported by an illustrative example.
- Caputo fractional derivatives,
- R-L integrals,
- fixed point methodology,
- Leray-Schauder alternative
Citation: Hasanen A. Hammad, Manuel De la Sen. Involvement of the fixed point technique for solving a fractional differential system[J]. AIMS Mathematics, 2022, 7(4): 7093-7105. doi: 10.3934/math.2022395

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Abstract

Some physical phenomena were described through fractional differential equations and compared with integer-order differential equations which have better results, which is why researchers of different areas have paid great attention to study this direction. So, in this manuscript, we discuss the existence and uniqueness of solutions to a system of fractional deferential equations (FDEs) under Riemann-Liouville (R-L) integral boundary conditions. The solution method is obtained by two basic rules, the first rule is the Leray-Schauder alternative and the second is the Banach contraction principle. Finally, the theoretical results are supported by an illustrative example.

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