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Abstrakty
Using the well-known monotone iterative technique together with the method of upper and lower solutions, the authors investigate the existence of extremal solutions to a class of coupled systems of nonlinear fractional differential equations involving the ψ–Caputo derivative with initial conditions. As applications of this work, two illustrative examples are presented.
Czasopismo
Rocznik
Tom
Strony
19--34
Opis fizyczny
Bibliogr. 46 poz.
Twórcy
autor
- Laboratory of Mathematics and Applied Sciences, University of Ghardaia, 47000 Algeria, Algeria
autor
- Laboratory of Mathematics and Applied Sciences, University of Ghardaia, 47000 Algeria, Algeria
autor
- Laboratory of Mathematics, Djillali Liabes University of Sidi-Bel-Abbes, Algeria
autor
- Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN 37403, USA
Bibliografia
- [1] S. Abbas, M. Benchohra, G.M. N'Guérékata, Topics in Fractional Differential Equations, Dev. Math., 27, Springer, New York, 2015.
- [2] S. Abbas, M. Benchohra, G.M.N'Guérékat, Advanced Fractional Differential and Integral Equations, Nova Sci. Publ., New York, 2014.
- [3] S. Abbas, M. Benchohra, J.R. Graef, J. Henderson, Implicit Fractional Differential and Integral Equations: Existence and Stability, De Gruyter, Berlin, 2018.
- [4] S. Abbas, M. Benchohra, N. Hamidi, J. Henderson, Caputo-Hadamard fractional differential equations in Banach spaces, Fract. Calc. Appl. Anal. 21 (2018) 1027-1045.
- [5] S. Abbas, M. Benchohra, B. Samet, Y. Zhou, Coupled implicit Caputo fractional q-difference systems, Adv. Difference Equ., Paper No. 527 (2019) 1-19.
- [6] R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional di_erential equations and inclusions, Acta Appl. Math. 109 (2010) 973-1033.
- [7] A. Aghajani, E. Pourhadi, J.J. Trujillo, Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces, Fract. Calc. Appl. Anal. 16 (2013) 962-977.
- [8] R. Almeida, A Caputo fractional derivative of a function with respect to another function, Commun. Nonlinear Sci. Numer. Simul. 44 (2017) 460{481. Coupled System of Nonlinear Fractional Differential Equations
- [9] R. Almeida, Fractional dfferential equations with mixed boundary conditions, Bull. Malays. Math. Sci. Soc. 42 (2019) 1687-1697.
- [10] R. Almeida, A.B. Malinowska, M.T.T. Monteiro, Fractional differential equations with a Caputo derivative with respect to a kernel function and their applications, Math. Meth. Appl. Sci. 41 (2018) 336-352.
- [11] R. Almeida, A.B. Malinowska, T. Odzijewicz, Optimal leader-follower control for the fractional opinion formation model, J. Optim. Theory Appl. 182 (2019) 1171-1185.
- [12] R. Almeida, M. Jleli, B. Samet, A numerical study of fractional relaxation-oscillation equations involving Caputo fractional derivative, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019) 1873-1891.
- [13] M. Al-Refai, M. Ali Hajji, Monotone iterative sequences for nonlinear boundary value problems of fractional order, Nonlinear Anal. 74 (2011) 3531-3539.
- [14] C. Chen, M. Bohner, B. Jia, Method of upper and lower solutions for nonlinear Caputo fractional diference equations and its applications, Fract. Calc. Appl. Anal. 22 (2019) 1307-1320.
- [15] C. Derbazi, Z. Baitiche, M. Benchohra, A. Cabada, Initial value problem for nonlinear fractional differential equations with Caputo derivative via monotone iterative technique, Axioms 9 (2020) 57. DOI:10.3390/axioms9020057
- [16] H. Fazli, H.G. Sun, S. Aghchi, Existence of extremal solutions of fractional Langevin equation involving nonlinear boundary conditions, Int. J. Comput. Math. 2020 (2020) 1-10.
- [17] R. Goreno, A.A. Kilbas, F. Mainardi, S. V. Rogosin, Mittag-Leffler Functions, Related Topics and Applications, Springer, New York, 2014.
- [18] R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- [19] F. Jarad, T. Abdeljawad, D. Baleanu, Caputo-type modification of the Hadamard fractional derivatives, Adv. Difference Equ. 2012 (142) (2012) 1-8.
- [20] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204, Elsevier, Amsterdam, 2006.
- [21] K.D. Kucche, A. Mali, J. Vanterler da C. Sousa, On the nonlinear Hilfer fractional differential equations. Comput. Appl. Math. 38 (2019) Art. 73, 1-25.
- [22] K.D. Kucche, A.D. Mali, Initial time di_erence quasilinearization method for fractional differential equations involving generalized Hilfer fractional derivative, Comput. Appl. Math. 39, Paper No. 31 (2020) 1-33.
- [23] X. Lin, Z. Zhao, Iterative technique for a third-order differential equation with three-point nonlinear boundary value conditions, Electron. J. Qual. Theory Differ. Equ. 2016, Paper No. 12 (2016) 1-10.
- [24] S. Liu, H. Li, Extremal system of solutions for a coupled system of nonlinear fractional differential equations by monotone iterative method, J. Nonlinear Sci. Appl. 9 (2016) 3310-3318.
- [25] Y. Luchko, J.J. Trujillo, Caputo-type modification of the Erdélyi-Kober fractional derivative, Fract. Calc. Appl. Anal. 10 (2007) 249-267.
- [26] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity, Imperial College Press, London, 2010.
- [27] M. Metwali, On some qualitative properties of integrable solutions for Cauchy-type problem of fractional order, J. Math. Appl. 40 (2017) 121-134.
- [28] K.S. Miller, B. Ross, An Introduction to Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
- [29] K.B. Oldham, Fractional differential equations in electrochemistry, Adv. Eng. Softw. 41 (2010) 9-12.
- [30] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
- [31] J. Sabatier, O.P. Agrawal, J.A.T. Machado, Advances in Fractional Calculus-Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, 2007.
- [32] B. Samet, H. Aydi, Lyapunov-type inequalities for an anti-periodic fractional boundary value problem involving Caputo fractional derivative, J. Inequal. Appl. 2018, Paper No. 286 (2018) 1-11.
- [33] W. El-Sayed, M. El-Borai, M. Metwali, N. Shemais, On the existence of continuous solutions of a nonlinear quadratic fractional integral equation, J. Advances Math. 19 (2020) 14-25.
- [34] V.E. Tarasov, Fractional Dynamics, Nonlinear Physical Science, Springer, Heidelberg, 2010.
- [35] V.E. Tarasov (Editor), Handbook of Fractional Calculus with Applications, Vol. 5, Applications in Physics, Part B, De Gruyter, Berlin, 2019.
- [36] G. Wang, R.P. Agarwal, A. Cabada, Existence results and the monotone iterative technique for systems of nonlinear fractional differential equations, Appl. Math. Lett. 25 (2012) 1019-1024.
- [37] G. Wang, W. Sudsutad, L. Zhang, J. Tariboon, Monotone iterative technique for a nonlinear fractional q-difference equation of Caputo type, Adv. Difference Equ., 2016, Paper No. 211 (2016) 1-11.
- [38] G.Wang, J. Qin, L. Zhang, D. Baleanu, Monotone iterative method for a nonlinear fractional conformable p-Laplacian differential system, Math. Meth. Appl. Sci. 2020, 1-11.
- [39] J. Wang, L. Lv, Y. Zhou, Ulam stability and data dependence for fractional differential equations with Caputo derivative, Electron. J. Qual. Theory Differ. Equ. 2011 (63) (2011) 1-10.
- [40] J. Wang, X. Li, E-Ulam type stability of fractional order ordinary differential equations, J. Appl. Math. Comput. 45 (2014) 449-459.
- [41] J.Wang, Y. Zhang, Ulam-Hyers-Mittag-Leffler stability of fractional-order delay differential equations, Optimization 63 (2014) 1181-1190.
- [42] N. Xu, W. Liu, Iterative solutions for a coupled system of fractional differential-integral equations with two-point boundary conditions, Appl. Math. Comput. 244 (2014) 903-911.
- [43] W. Yang, Monotone iterative technique for a coupled system of nonlinear Hadamard fractional differential equations, J. Appl. Math. Comput. 59 (2019) 585-596.
- [44] S. Zhang, Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives, Nonlinear Anal. 71 (2009) 2087-2093.
- [45] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.
- [46] Y. Zhou, Fractional Evolution Equations and Inclusions: Analysis and Control, Elsevier, 2016.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0ec614b5-d3c9-43af-a925-fb18648d7a55