Lachouri, Adel, Ardjouni, Abdelouaheb, Gouri, Nesrine, Ali Khelil, Kamel. (1400). Existence and stability analysis for nonlinear ψ-Hilfer fractional differential equations with nonlocal integral boundary conditions. هنرهای کاربردی, 13(1), 2617-2633. doi: 10.22075/ijnaa.2021.24122.2674
Adel Lachouri; Abdelouaheb Ardjouni; Nesrine Gouri; Kamel Ali Khelil. "Existence and stability analysis for nonlinear ψ-Hilfer fractional differential equations with nonlocal integral boundary conditions". هنرهای کاربردی, 13, 1, 1400, 2617-2633. doi: 10.22075/ijnaa.2021.24122.2674
Lachouri, Adel, Ardjouni, Abdelouaheb, Gouri, Nesrine, Ali Khelil, Kamel. (1400). 'Existence and stability analysis for nonlinear ψ-Hilfer fractional differential equations with nonlocal integral boundary conditions', هنرهای کاربردی, 13(1), pp. 2617-2633. doi: 10.22075/ijnaa.2021.24122.2674
Lachouri, Adel, Ardjouni, Abdelouaheb, Gouri, Nesrine, Ali Khelil, Kamel. Existence and stability analysis for nonlinear ψ-Hilfer fractional differential equations with nonlocal integral boundary conditions. هنرهای کاربردی, 1400; 13(1): 2617-2633. doi: 10.22075/ijnaa.2021.24122.2674

Existence and stability analysis for nonlinear ψ-Hilfer fractional differential equations with nonlocal integral boundary conditions

International Journal of Nonlinear Analysis and Applications
مقاله 214، دوره 13، شماره 1، خرداد 2022، صفحه 2617-2633    اصل مقاله (400.09 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24122.2674
نویسندگان
Adel Lachouri* 1؛ Abdelouaheb Ardjouni2؛ Nesrine Gouri1؛ Kamel Ali Khelil3
1Department of Mathematics, Faculty of Sciences, University of Annaba, Annaba, Algeria
2Department of Mathematics and Informatics, University of Souk Ahras, Souk Ahras, Algeria
3Laboratory of Analysis and Control of Differential Equations,University of 8 May 1945 Guelma, Algeria
چکیده
In this paper, we study the existence and uniqueness of mild solutions for nonlinear fractional differential equations subject to nonlocal integral boundary conditions in the frame of a ψ-Hilfer fractional derivative. Further, we discuss different kinds of stability of Ulam-Hyers for mild solutions to the given problem. Using the fixed point theorems together with generalized Gronwall inequality the desired outcomes are proven. The obtained results generalize many previous works that contain special cases of function ψ. At the end, some pertinent examples demonstrating the effectiveness of the theoretical results are presented.
کلیدواژه‌ها
ψ-Hilfer fractional derivative؛ mild solution؛ Ulam-Hyers stability؛ fixed point theorems
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