Existence criteria for fractional differential equations using the topological degree method

Kottakkaran Sooppy Nisar; Suliman Alsaeed; Kalimuthu Kaliraj; Chokkalingam Ravichandran; Wedad Albalawi; Abdel-Haleem Abdel-Aty; Kottakkaran Sooppy Nisar; Suliman Alsaeed; Kalimuthu Kaliraj; Chokkalingam Ravichandran; Wedad Albalawi; Abdel-Haleem Abdel-Aty

doi:10.3934/math.20231117

AIMS Mathematics

2023, Volume 8, Issue 9: 21914-21928. doi: 10.3934/math.20231117

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Existence criteria for fractional differential equations using the topological degree method

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Applied Sciences College, Department of Mathematical Sciences, Umm Al-Qura University, P.O. Box 715, Makkah 21955, Saudi Arabia
3.
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai 600005, India
4.
Department of Mathematics, Kongunadu Arts and Science College, Coimbatore-641029, India
5.
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
6.
Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia

Received: 24 March 2023 Revised: 16 June 2023 Accepted: 20 June 2023 Published: 10 July 2023
MSC : 34A08, 37C25, 34K10, 34K37

In this work, we analyze the fractional order by using the Caputo-Hadamard fractional derivative under the Robin boundary condition. The topological degree method combined with the fixed point methodology produces the desired results. Finally to show how the key findings may be utilized, applications are presented.
- fractional calculus,
- integro-differential equation,
- fixed point techniques,
- topological degree method
Citation: Kottakkaran Sooppy Nisar, Suliman Alsaeed, Kalimuthu Kaliraj, Chokkalingam Ravichandran, Wedad Albalawi, Abdel-Haleem Abdel-Aty. Existence criteria for fractional differential equations using the topological degree method[J]. AIMS Mathematics, 2023, 8(9): 21914-21928. doi: 10.3934/math.20231117

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Abstract

In this work, we analyze the fractional order by using the Caputo-Hadamard fractional derivative under the Robin boundary condition. The topological degree method combined with the fixed point methodology produces the desired results. Finally to show how the key findings may be utilized, applications are presented.

References

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