EXISTENCE OF SOLUTIONS AND ULAM STABILITY OF HILFER-HADAMARD SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM

Jakgrit Sompong; Ekkarath Thailert; Sotiris K. Ntouyas; Ugyen Samdrup Tshering

doi:10.11948/20240290

2025 Volume 15 Issue 3

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Jakgrit Sompong, Ekkarath Thailert, Sotiris K. Ntouyas, Ugyen Samdrup Tshering. EXISTENCE OF SOLUTIONS AND ULAM STABILITY OF HILFER-HADAMARD SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1536-1562. doi: 10.11948/20240290

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Jakgrit Sompong, Ekkarath Thailert, Sotiris K. Ntouyas, Ugyen Samdrup Tshering. EXISTENCE OF SOLUTIONS AND ULAM STABILITY OF HILFER-HADAMARD SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1536-1562. doi: 10.11948/20240290

EXISTENCE OF SOLUTIONS AND ULAM STABILITY OF HILFER-HADAMARD SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-POINT FRACTIONAL INTEGRAL BOUNDARY VALUE PROBLEM

1.
Department of Mathematics, Naresuan University 65000, Phitsanulok, Thailand
2.
Research Center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok 65000, Thailand
3.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
4.
Department of Mathematics, Royal University of Bhutan, Bhutan

Author Bio: Email: jakgrits@nu.ac.th(J. Sompong); Email: ekkaratht@nu.ac.th(E. Thailert); Email: sntouyas@uoi.gr(S. K. Ntouyas)
Corresponding author: Email: ugyens64@nu.ac.th(U. S. Tshering)

Abstract

Abstract

In this paper, we study the existence and uniqueness of solutions for the boundary value problem of Hilfer-Hadamard sequential fractional differential equations via fixed point theorems. The existence of a solution is proved by the Krasnoselskii fixed point theorem, the Leray-Schauder alternative, and the Leray-Schauder nonlinear alternative fixed point theorem. Moreover, we prove the uniqueness of the solution using the Banach contraction principle. We also discuss the Ulam-Hyers, Ulam-Hyers-Rassias, generalized Ulam-Hyers and generalized Ulam-Hyers-Rassias stability for the problem. Illustrative examples are also provided.
- Fractional differential equations /
- Hilfer-Hadamard fractional derivative /
- fixed point theory /
- Ulam-Hyers stability /
- Ulam-Hyers-Rassias stability
MSC: 26A33, 34A08, 34B15

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References

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