Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions

Zaid Laadjal; Fahd Jarad; Zaid Laadjal; Fahd Jarad

doi:10.3934/math.2023059

AIMS Mathematics

2023, Volume 8, Issue 1: 1172-1194. doi: 10.3934/math.2023059

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Research article

Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions

Zaid Laadjal ^{1
,
,},
Fahd Jarad ^{2,3
,
,}

1.
Department of Mathematics and Computer Science, University Center of Illizi, IIlizi, 33000, Algeria
2.
Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 01 July 2022 Revised: 30 September 2022 Accepted: 07 October 2022 Published: 18 October 2022
MSC : 26A33, 34A08, 34A12, 45J05

In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.
Citation: Zaid Laadjal, Fahd Jarad. Existence, uniqueness and stability of solutions for generalized proportional fractional hybrid integro-differential equations with Dirichlet boundary conditions[J]. AIMS Mathematics, 2023, 8(1): 1172-1194. doi: 10.3934/math.2023059

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Abstract

In this work, the existence of solutions for nonlinear hybrid fractional integro-differential equations involving generalized proportional fractional (GPF) derivative of Caputo-Liouville-type and multi-term of GPF integrals of Reimann-Liouville type with Dirichlet boundary conditions is investigated. The analysis is accomplished with the aid of the Dhage's fixed point theorem with three operators and the lower regularized incomplete gamma function. Further, the uniqueness of solutions and their Ulam-Hyers-Rassias stability to a special case of the suggested hybrid problem are discussed. For the sake of corroborating the obtained results, an illustrative example is presented.

References

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