Applying fixed point techniques to solve fractional differential inclusions under new boundary conditions

Murugesan Manigandan; Kannan Manikandan; Hasanen A. Hammad; Manuel De la Sen; Murugesan Manigandan; Kannan Manikandan; Hasanen A. Hammad; Manuel De la Sen

doi:10.3934/math.2024750

AIMS Mathematics

2024, Volume 9, Issue 6: 15505-15542. doi: 10.3934/math.2024750

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Research article

Applying fixed point techniques to solve fractional differential inclusions under new boundary conditions

1.
Center for Computational Modeling, Chennai Institute of Technology, Chennai-600 069, Tamilnadu, India
2.
Department of Mathematics, College of Science, Qassim University, Buraydah 52571, Saudi Arabia
3.
Department of Mathematics, Saveetha School of Engineering, SIMATS, Saveetha University, Chennai 602105, India
4.
Department of Mathematics, Faculty of Science, Sohag University, Sohag 82524, Egypt
5.
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country, 48940-Leioa (Bizkaia), Spain

Received: 02 February 2024 Revised: 16 April 2024 Accepted: 19 April 2024 Published: 29 April 2024
MSC : 34A05, 34B15, 47H10

Many scholars have lately explored fractional-order boundary value issues with a variety of conditions, including classical, nonlocal, multipoint, periodic/anti-periodic, fractional-order, and integral boundary conditions. In this manuscript, the existence and uniqueness of solutions to sequential fractional differential inclusions via a novel set of nonlocal boundary conditions were investigated. The existence results were presented under a new class of nonlocal boundary conditions, Carathéodory functions, and Lipschitz mappings. Further, fixed-point techniques have been applied to study the existence of results under convex and non-convex multi-valued mappings. Ultimately, to support our findings, we analyzed an illustrative example.
- fixed point technique,
- Carathéodory function,
- existence solution,
- fractional derivatives,
- sequential differential inclusions
Citation: Murugesan Manigandan, Kannan Manikandan, Hasanen A. Hammad, Manuel De la Sen. Applying fixed point techniques to solve fractional differential inclusions under new boundary conditions[J]. AIMS Mathematics, 2024, 9(6): 15505-15542. doi: 10.3934/math.2024750

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Abstract

Many scholars have lately explored fractional-order boundary value issues with a variety of conditions, including classical, nonlocal, multipoint, periodic/anti-periodic, fractional-order, and integral boundary conditions. In this manuscript, the existence and uniqueness of solutions to sequential fractional differential inclusions via a novel set of nonlocal boundary conditions were investigated. The existence results were presented under a new class of nonlocal boundary conditions, Carathéodory functions, and Lipschitz mappings. Further, fixed-point techniques have been applied to study the existence of results under convex and non-convex multi-valued mappings. Ultimately, to support our findings, we analyzed an illustrative example.

References

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