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Picard iterative approach for $psi$-Hilfer fractional differential problem | ||
| Journal of Mathematical Modeling | ||
| مقاله 10، دوره 11، شماره 3، دی 2023، صفحه 573-585 اصل مقاله (175.7 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.24626.2201 | ||
| نویسندگان | ||
| Eknath D. Pawar* 1؛ Ramkrishna M. Dhaigude2 | ||
| 1Department of Mathematics, Dr Babasaheb Ambedkar Marathwada University, Aurangabad, India | ||
| 2Department of Mathematics, Government Vidarbh Institute of Science & Humanities, Amaravati, (M.S) India | ||
| چکیده | ||
| In present work, we discuss local existance and uniqueness of solution to the $\psi-$Hilfer fractional differential problem. By using the Picard successive approximations, we construct a computable iterative scheme uniformly approximating solution. Two illustrative examples are given to support our findings. | ||
| کلیدواژهها | ||
| Fractional calculus؛ $\psi$−Hilfer fractional derivative؛ Picard’s iterative scheme؛ convergence | ||
| مراجع | ||
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[1] M.S. Abdo, S.K. Panchal, Fractional integro-differential equations involving ψ− Hilfer fractional derivative, Adv. Appl. Math. Mech. 11 (2019) 338–359. [2] M.A. Almalahi, M.S. Abdo, S.K. Panchal ψ-Hilfer fractional functional differential equation by Picard operator method, J. Appl. Nonlinear Dynam. 9 (2020) 685–702. [3] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Comm. Nonlinear Sci. Numer. Sinulat., 44 (2017) 460–481. [4] T.M. Atanackovic, S. Pilipovic, B. Stankovic, D. Zorica, Fractional calculus with applications in mechanics: Vibrations and diffusion processes, Wiley-ISTE, London, Hoboken, 2014. [5] S.P. Bhairat, Existence and continuation of solutions of Hilfer fractional differential equations, J. Math. Model. 7 (2019) 1–20. [6] S.P. Bhairat, On local existence of solution for nonlinear Hilfer fractional differential equation, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 29 (2022) 363–374. [7] S.P. Bhairat, New approach to existence of solution for weighted Cauchy-type problem, J. Math. Model. 8 (2020) 377–391. [8] D. Delbosco, L. Rodino, Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl. 204 (1996) 609–625. [9] K. Diethelm, The Analysis of Fractional Differential Equations, Lecture Notes in Mathematics, Springer–Verlag Berlin Heidelberg, 2010. [10] D.B. Dhaigude, S.P. Bhairat, Existence and uniqueness of solution of Cauchy-type problem for Hilfer fractional differential equations, Comnun. Appl. Anal. 22 (2018) 121–134. [11] D.B. Dhaigude, S.P. Bhairat, Local existence and uniqueness of solution of Hilfer fractional differ- ential equations, Nonlinear Dyn. Syst. Theory. 18 (2018) 144–153. [12] K.M. Furati, M.D. Kassim,Existence and uniqueness for a problem involving Hilfer fractional derivative, Computer Math. Appl. 64 (2012) 1616–1626. [13] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000. [14] A.A. Kilbas, H.M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Math Stud, 204 Elsevier, Amsterdam, 2006. [15] K.D. Kucche, A.D. Mali, J. Vanterler da C. Sousa, On the nonlinear ψ-Hilfer fractional differential equations, Comput. Appl. Math., 38 (2019) 73. [16] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, an Introduction to Mathe- matical Model, Imperical College Press, World Scientific Publishing, London, 2010. [17] F. Norouzi, G.M. N’Guerekata A study of ψ−Hilfer fractional differential system with application in financial crisis, Chaos Solitons Fractals 6 (2021) 100056. [18] I. Podlubny, Fractional Differential Equations, Academic Press, 1998. [19] A. Salim, M. Benchohra, J.R. Graef, J.E. Lazreg, Initial value problem for hybrid ψ-Hilfer frac- tional implicit differential equations, J. Fixed Point Theory Appl. 24 (2022) 1–14. [20] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives - Theory and Appli- cations, Gordon and Breach, 1993. [21] C. Sousa, E.C. de Oliveira, Leibniz type rule: ψ-Hilfer fractional operator, Comnun. Nonlinear Sci. Numer. Sinulat. 77 (2019) 305–311. [22] H.G. Sun, Y. Zhang, D. Baleanu, W. Chena, Y.Q. Chene, A new collection of real world applica- tions of fractional calculus in science and engineering, Comnun. Nonlinear Sci. Numer. Sinulat. 64 (2018) 213–231. [23] R. Toledo-Henrnandez, V. Rico-Ramirez, G.A. Iglesias-Silva, U.M. Diwekar, A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions, Chem. Eng. Sci., 117 (2014) 217–228. [24] J. Vanterler da C. Sousa, E. Capelas de Oliveira, On the ψHilfer fractional derivative, Comnun. Nonlinear Sci. Numer. Sinulat. 60 (2018) 72–91. [25] J. Vanterler da C. Sousa, E. Capelas Oliveira, A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator, Diff. Equ. Appl. 11 (2019), 87–106. [26] N. Vieira, M.M. Rodregues, M. Ferriera, Fractional gradient methods via ψ−Hilfer derivative, Fractal Fract. 7 (2023) 275. [27] X. Yang and Y. Liu, Picard iterative processes for initial value problems of singular fractional differential equations, Adv. Differ. Equat. 2014 (2014) 102. | ||
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