Abstract:
In this article, we prove the existence and approximation of solutions of the initial value problems of nonlinear hybrid Caputo fractional integro-differential equations. The main tool employed here is the Dhage iteration principle in a partially ordered normed linear space. An example is also given to illustrate the main results.
Keywords:
approximating solutions, initial value problems, Dhage iteration principle, hybrid fixed point theorem.
This publication is cited in the following 15 articles:
Lamia Harkat, Karima Bessioud, Abdelouaheb Ardjouni, “Existence and Ulam stability of mild solutions for nonlinear fractional integro-differential equations in a Banach space”, São Paulo J. Math. Sci., 18:1 (2024), 258
Huda A. Salim, Bashaer M. Abdali, Fajir A. Abdulkhaleq, Osama H. Mohammed, “Perturbation iteration transform method for solving fractional order integro-differential equation”, Partial Differential Equations in Applied Mathematics, 11 (2024), 100874
S. Akhlaghi, M. Tavassoli Kajani, M. Allame, Guotao Wang, “Numerical Solution of Fractional Order Integro-Differential Equations via Müntz Orthogonal Functions”, Journal of Mathematics, 2023 (2023), 1
Jehad Alzabut, A. George Maria Selvam, Dhakshinamoorthy Vignesh, Yousef Gholami, “Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order”, International Journal of Nonlinear Sciences and Numerical Simulation, 24:6 (2023), 2263
Adel Lachouri, Abdelouaheb Ardjouni, Ahcene Djoudi, “Existence results for nonlinear sequential Caputo and Caputo-Hadamard fractional differential equations with three-point boundary conditions in Banach spaces”, Filomat, 36:14 (2022), 4717
Wafa Shammakh, A. George Maria Selvam, Vignesh Dhakshinamoorthy, Jehad Alzabut, “Stability of Boundary Value Discrete Fractional Hybrid Equation of Second Type with Application to Heat Transfer with Fins”, Symmetry, 14:9 (2022), 1877
Abdelouaheb ARDJOUNİ, Abderrahim GUERFİ, “On the existence of mild solutions for totally nonlinear Caputo-Hadamard fractional differential equations”, Results in Nonlinear Analysis, 5:2 (2022), 161
Abdellatif Boutiara, Mohammed M. Matar, Mohammed K. A. Kaabar, Francisco Martínez, Sina Etemad, Shahram Rezapour, Santosh Kumar, “Some Qualitative Analyses of Neutral Functional Delay Differential Equation with Generalized Caputo Operator”, Journal of Function Spaces, 2021 (2021), 1
Abdelouaheb Ardjouni, Moussa Haoues, “Existence and monotonicity of positive solutions for hybridCaputo-Hadamard fractional integro-differential equations”, Malaya J. Mat., 9:04 (2021), 168
Abderrahim GUERFİ, Abdelouaheb ARDJOUNİ, “Existence and uniqueness of mild solutions for nonlinear hybrid Caputo fractional integro-differential equations via fixed point theorems”, Results in Nonlinear Analysis, 4:4 (2021), 207
Adel Lachouri, Abdelouaheb Ardjouni, Ahcene Djoudi, “Initial value problems of nonlinear fractional differential equations with two orders”, Ann Univ Ferrara, 67:2 (2021), 369
Mahmoud Bousselsal, Azzeddine Bellour, “Existence and asymptotic stability of continuous solutions for integral equations of product type”, J. Innov. Appl. Math. Comput. Sci, 1:1 (2021), 31
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