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Existence, uniqueness and finite-time stability of solutions for Ψ-Caputo fractional differential equations with time delay | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 فروردین 1402 اصل مقاله (1.13 MB) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2023.52613.2209 | ||
| نویسندگان | ||
Naoufel Hatime1؛ Said Melliani1؛ Ali El Mfadel  1؛ Mhamed Elomari2
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| 1Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, Beni Mellal, Morocco | ||
| 2Laboratory of Applied Mathematics Scientific Calculus, Sultan Moulay Slimane University, BP 523, 23000, Beni Mellal, 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\in (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 heat transfer model, a new criterion for finite time stability and some estimate results of solutions with time delay are derived. In addition, we give some specific examples with graphs and numerical experiment to illustrate the obtained results. More importantly, the comparison of model predictions versus experimental data, classical model and non-delayed model show the effectiveness of our proposed model with a reasonable precision. | ||
| کلیدواژه‌ها | ||
| Newton's law of cooling equation؛ $Psi$-Caputo fractional derivative؛ delay؛ modelling nature | ||
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آمار تعداد مشاهده مقاله: 73 تعداد دریافت فایل اصل مقاله: 74 |
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