Ayyadi, Souad, Alzabut, Jehad, Selvam, A. George, Vignesh, D.. (1402). On stability results for a nonlinear generalized fractional hybrid pantograph equation involving deformable derivative. هنرهای کاربردی, 14(8), 1-14. doi: 10.22075/ijnaa.2023.26647.3376
Souad Ayyadi; Jehad Alzabut; A. George M Selvam; D. Vignesh. "On stability results for a nonlinear generalized fractional hybrid pantograph equation involving deformable derivative". هنرهای کاربردی, 14, 8, 1402, 1-14. doi: 10.22075/ijnaa.2023.26647.3376
Ayyadi, Souad, Alzabut, Jehad, Selvam, A. George, Vignesh, D.. (1402). 'On stability results for a nonlinear generalized fractional hybrid pantograph equation involving deformable derivative', هنرهای کاربردی, 14(8), pp. 1-14. doi: 10.22075/ijnaa.2023.26647.3376
Ayyadi, Souad, Alzabut, Jehad, Selvam, A. George, Vignesh, D.. On stability results for a nonlinear generalized fractional hybrid pantograph equation involving deformable derivative. هنرهای کاربردی, 1402; 14(8): 1-14. doi: 10.22075/ijnaa.2023.26647.3376

On stability results for a nonlinear generalized fractional hybrid pantograph equation involving deformable derivative

International Journal of Nonlinear Analysis and Applications
مقاله 1، دوره 14، شماره 8، آبان 2023، صفحه 1-14    اصل مقاله (635.19 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.26647.3376
نویسندگان
Souad Ayyadi1؛ Jehad Alzabut* 2، 3؛ A. George M Selvam4؛ D. Vignesh5
1Acoustics and Civil Engineering Laboratory Djilali Bounaama University-Khemis, Miliana, Algeria
2Department of Mathematics and Sciences, Prince Sultan University, 11586 Riyadh, Saudi Arabia
3Department of Industrial Engineering,\ OST\.{I}M Technical University, Ankara 06374, Turkey
4Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur-635601, Tamil Nadu, India
5Cyber Security and Digital Industrial Revolution Centre, National Defence University of Malaysia, Kem Sungai Besi, 57000, Kuala Lumpur, Malaysia
چکیده
The pantograph equation is a special type of delay differential equation with applications in quantum mechanics and electrodynamics. A generalized hybrid pantograph equation of fractional order involving deformable derivative is considered in this work to carry out the stability analysis. The existence of solutions is established by employing the measure of noncompactness and Darbo's fixed point theorem while the contraction mapping principle is used for proving the uniqueness of the solution.  The link between the right-hand term of the given equation and the order of the deformable derivative is established. The paper presents the results on Ulam-Hyers stability and the generalized Ulam-Hyers stability of the proposed equation. Numerical simulations are provided to demonstrate the performed theoretical analysis.
کلیدواژه‌ها
Deformable derivative؛ Pantograph equations؛ Darbo fixed point؛ Initial value problem
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