Hilfer iterated-integro-differential equations and boundary conditions

Sunisa Theswan; Ayub Samadi; Sotiris K. Ntouyas; Jessada Tariboon; Sunisa Theswan; Ayub Samadi; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.2022770

AIMS Mathematics

2022, Volume 7, Issue 8: 13945-13962. doi: 10.3934/math.2022770

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Hilfer iterated-integro-differential equations and boundary conditions

1.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2.
Department of Mathematics, Miyaneh Branch, Islamic Azad University, Miyaneh, Iran
3.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
4.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematices, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 26 January 2022 Revised: 11 April 2022 Accepted: 21 April 2022 Published: 26 May 2022
MSC : 34A08, 34B15

In this research, a new class of fractional boundary value problems is introduced and studied, which combine Hilfer fractional derivatives with iterated Riemann-Liouville and Hadamard fractional integrals boundary conditions. Existence and uniqueness results are obtained by using standard tools from fixed point theory. The obtained results are well illustrated by numerical examples.
Citation: Sunisa Theswan, Ayub Samadi, Sotiris K. Ntouyas, Jessada Tariboon. Hilfer iterated-integro-differential equations and boundary conditions[J]. AIMS Mathematics, 2022, 7(8): 13945-13962. doi: 10.3934/math.2022770

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Abstract

In this research, a new class of fractional boundary value problems is introduced and studied, which combine Hilfer fractional derivatives with iterated Riemann-Liouville and Hadamard fractional integrals boundary conditions. Existence and uniqueness results are obtained by using standard tools from fixed point theory. The obtained results are well illustrated by numerical examples.

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