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Hatime, Naoufel, Melliani, Said, El Mfadel, Ali, Elomari, Mhamed. (1402). Existence, uniqueness, and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay. سامانه مدیریت نشریات علمی, 11(4), 785-802. doi: 10.22034/cmde.2023.52613.2209
Naoufel Hatime; Said Melliani; Ali El Mfadel; Mhamed Elomari. "Existence, uniqueness, and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay". سامانه مدیریت نشریات علمی, 11, 4, 1402, 785-802. doi: 10.22034/cmde.2023.52613.2209
Hatime, Naoufel, Melliani, Said, El Mfadel, Ali, Elomari, Mhamed. (1402). 'Existence, uniqueness, and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay', سامانه مدیریت نشریات علمی, 11(4), pp. 785-802. doi: 10.22034/cmde.2023.52613.2209
Hatime, Naoufel, Melliani, Said, El Mfadel, Ali, Elomari, Mhamed. Existence, uniqueness, and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay. سامانه مدیریت نشریات علمی, 1402; 11(4): 785-802. doi: 10.22034/cmde.2023.52613.2209

Existence, uniqueness, and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay

Computational Methods for Differential Equations
مقاله 9، دوره 11، شماره 4، مهر 2023، صفحه 785-802    اصل مقاله (391.28 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.52613.2209
نویسندگان
Naoufel Hatime1؛ Said Melliani1؛ Ali El Mfadel* 1، 2؛ Mhamed Elomari1
1LMACS Laboratory, Sultan Moulay Slimane University, Beni Mellal, Morocco.
2Superior School of Technology, Sultan Moulay Slimane University, Khenifra, Morocco.
چکیده
In this paper, we study the existence, uniqueness, and finite-time stability results for fractional delayed Newton cooling law equation involving Ψ-Caputo fractional derivatives of order α ∈ (0, 1). By using Banach fixed point theorem, Henry Gronwall type retarded integral inequalities, and some techniques of Ψ-Caputo fractional calculus, we establish the existence and uniqueness of solutions for our proposed model. Based on the heat transfer model, a new criterion for finite time stability and some estimated results of solutions with time delay are derived. In addition, we give some specific examples with graphs and numerical experiments to illustrate the obtained results. More importantly, the comparison of model predictions versus experimental data, classical model, and non-delayed model shows the effectiveness of our proposed model with a reasonable precision.
کلیدواژه‌ها
Newton’s law of cooling equation؛ Ψ-Caputo fractional derivative؛ delay؛ Modelling nature
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