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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
مراجع
  • [1] W. M. Abd-Elhameed, J. A. T. Machado, and Y. H. Youssri, Hypergeometric fractional derivatives formula of shifted Chebyshev polynomials: tau algorithm for a type of fractional delay differential equations, International Journal of Nonlinear Sciences and Numerical Simulation, 23(7-8) (2022), 1253-1268.
  • [2] R. P. Agarwal, S. Hristova, and D. O’Regan, A survey of Lyapunov functions stability and impulsive Caputo fractional differential equations, Fract. Calc. Appl. Anal., 19 (2015), 290–318.
  • [3] R. P. Agarwal, S. K. Ntouyas, B. Ahmad, and A. K. Alzahrani, Hadamard-type fractional functional differential equations and inclusions with retarded and advanced arguments, Advances in Difference Equations., 1 (2016), 1–15.
  • [4] R. Almeida, Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul., 44 (2017), 460–481.
  • [5] R. Almeida, What is the best fractional derivative to fit data?, Applicable Analysis and Discrete Mathematics., 11(2) (2017), 358–368.
  • [6] R. Almeida, A. B. Malinowska, and M. Monteiro, Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications, Mathematical Methods in the Applied Sciences., 41(1)(2018), 336–352.
  • [7] R. Almeida, Functional differential equations involving the Ψ-Caputo fractional derivative, Fractal and Fractional., 4(2)(2020), 1–10.
  • [8] W. A. Alsadi, M. Hussein, and T. Q. Abdullah, Existence and stability criterion for the results of fractional order φp-Laplacian operator boundary value problem, Computational Methods for Differential Equations, 9(4) (2021), 1042-1058.
  • [9] S. Banach, Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fund. Math., 3 (1922), 133–181.
  • [10] R. B. Banks, T. Towing Icebergs, and F. Dominoes, Other Adventures in Applied Mathematics, Princeton Uni- versity Press, Princeton (1998).
  • [11] U. Besson, The History of the Cooling Law: When the Search for Simplicity can be an Obstacle, Sci & Educ, 21 (2012), 1085–1110.
  • [12] F. Brauer, Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling, 2(2) (2017), 113- 127.
  • [13] M. I. Davidzon, Newton’s law of cooling and its interpretation, Int J Heat Mass Transf., 21(55) (2012), 5397-5402.
  • [14] P. Dorato, Short time stability in linear time-varying systems, In: Proceedings of the IRE International Convention Record., 4 (1961), 83–87.
  • [15] P. Dorato, An Overview of Finite-Time Stability, Current Trends in Nonlinear Systems and Control., 3(2006), 185–194.
  • [16] A. El Mfadel, S. Melliani, and M. Elomari, Existence and uniqueness results for Caputo fractional boundary value problems involving the p-Laplacian operator, U.P.B. Sci. Bull. Series A., 84(1) (2022), 37-46 .
  • [17] A. El Mfadel, S. Melliani, and M. Elomari, New existence results for nonlinear functional hybrid differential equations involving the Ψ Caputo fractional derivative, Results in Nonlinear Analysis., 5(1) (2022), 78-86.
  • [18] A. El Mfadel, S. Melliani, and M. Elomari, Existence results for nonlocal Cauchy problem of nonlinear Ψ Caputo type fractional differential equations via topological degree methods, Advances in the Theory of Nonlinear Analysis and its Application., 6(2) (2022), 270-279.
  • [19] A. El Mfadel, S. Melliani, and M. Elomari, Existence of solutions for nonlinear Ψ Caputo-type fractional hybrid differential equations with periodic boundary conditions, Asia Pac. J. Math. (2022).
  • [20] T. Erneux, Applied Delay Differential Equations, No. 3 in Surveys and Tutorials in the Applied Mathematical Sciences., Springer, New York, 2009.
  • [21] F. Gieseking, Newton’s Law of Cooling An Experimental Investigation, The University of Georgia. Mathematics Education, EMAT, 4680 (2022), 6680.
  • [22] D. E. Gratie, B. Iancu, and I. Petre, ODE analysis of biological systems, Formal Methods for Dynamical Systems: 13th International School on Formal Methods for the Design of Computer, Communication, and Software Systems, SFM 2013, Bertinoro, Italy, Advanced Lectures, (2013), 29-62.
  • [23] R. M. Hafez and Y. H. Youssri, Shifted Gegenbauer-Gauss collocation method for solving fractional neutral functional-differential equations with proportional delays, Kragujevac Journal of Mathematics, 46(6) (2022), 981- 996.
  • [24] R. Hilfer, Applications of Fractional Calculus in Physics .Singapore, 2000.
  • [25] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo , Theory and Applications of Fractional Differential Equations. North-Holland Mathematical studies 204. Ed van Mill. Elsevier Science B.V. Amsterdam, (2006).
  • [26] W. O. Kermack and AG. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. Lond., 11(5) (1927), 700–721.
  • [27] G. A. Koch-Noble, Drugs in the Classroom: Using Pharmacokinetics to Introduce Biomathematical Modeling, Mathematical Modelling of Natural Phenomena., 6(6) (2011), 227-244.
  • [28] M. A. Khanday, A. Rafiq, and K. Nazir, Mathematical models for drug diffusion through the compartments of blood and tissue medium, Alexandria Journal of Medicine., 53(3) (2017), 245-249.
  • [29] D. Khusainov and G. Shuklin, Linear autonomous time-delay system with permutation matrices solving., Stud. Univ. Zilina Math.Ser., 17 (2013), 101-108.
  • [30] D. Khusainov and G. Shuklin, Relative controllability in systems with pure delay, Int. Appl. Mech., 41(2) (2005), 210-221.
  • [31] C. Leinbach, Beyond Newton’s law of cooling–estimation of time since death, International Journal of Mathemat- ical Education in Science and Technology., 42(6) (2011), 765-774.
  • [32] M. Li and J. Wang, Finite time stability of fractional delay differential equations, Appl. Math. Lett., 64 (2017), 170-176.
  • [33] A. J. Lotka, Elements of Physical Biology, Williams and Wilkins Company, 1925.
  • [34] Y. Luchko and J. J. Trujillo, Caputo-type modification of the Erdelyi-Kober fractional derivative, Fract. Calc. Appl. Anal., 10 (2007), 249-267.
  • [35] Z. Luo, W. Wei, and J. Wang, Finite time stability of semilinear delay differential equations. Nonlinear Dyn., 89 (2017), 713–722.
  • [36] T.K. Marshall and E.F. Hoare, Estimating the time of death: The rectal cooling after death and its mathematical expression. II. The use of the cooling formula in the study of post mortem body cooling. III. The use of the body temperature in estimating the time of death, J. Forensic Sci., 7 (1962), 56-81.
  • [37] L. Menten and M. Michaelis, Die kinetik der invertinwirkung. Biochem, 49 (1913), 333–369.
  • [38] W. G. Miller and R, A. Alberty, Kinetics of the reversible michaelis-menten mechanism and the applicability of the steady-state approximation, Journal of the American Chemical Society., 80(19) (1958), 5146–5151.
  • [39] I. Newton, The Mathematical Beginnings of Natural Philosophy Optics, Optical Lectures, (Selected Topics) Leningrad., (1929), 66-71.
  • [40] W. E. Ricker, Computation and interpretation of biological statistics of fish populations, Bull. Fish. Res. Bd., Can, 191 (1975), 1-382.
  • [41] M. B. Schaefer, Some aspects of the dynamics of populations important to the management of the commercial marine fisheries, Bulletin of the Inter-American Tropical Tuna. Commission., 1 (1954), 25–56.
  • [42] H. Smith, An Introduction to Delay Differential Equations with Applications to the Life Sciences, New York, NY: Springer New York, (2011), 119-130.
  • [43] J. Sousa and E. Capelas, A Gronwall inequality and the Cauchy-type problem by means of Ψ-Hilfer operator, Differ. Equ. Appl., 11 (2019), 87-106.
  • [44] V. Volterra, Animal ecology, In: Chapman, R.N.McGraw-Hill, New York, (1926), 409-448.
  • [45] H. Ye and J. Gao, Henry–Gronwall type retarded integral inequalities and their applications to fractional differential equations with delay, Applied Mathematics and Computation., 218(8) (2011), 4152-4160.
  • [46] Y. H. Youssri, S. Sayed, A. S. Mohamed, E. Aboeldahab and W. M. Abd-Elhameed, Modified Lucas polynomials for the numerical treatment of second-order boundary value problems. Computational Methods for Differential Equations, 11(1) (2023), 12-31.
  • [47] Y. H. Youssri and A. G. Atta, Spectral Collocation Approach via Normalized Shifted Jacobi Polynomials for the Nonlinear Lane-Emden Equation with Fractal-Fractional Derivative, Fractal and Fractional, 7(2) (2023), 133.
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