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Successive Approximations for Caputo-Fabrizio Fractional Differential Equations


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[1] ABBAS, S.—ARARA, A.—BENCHOHRA, M.: Global convergence of successive approximations for abstract semilinear differential equations, PanAmer. Math. J. 29 (2019), no. 1, 17–31. Search in Google Scholar

[2] ABBAS, S.—BENCHOHRA, M.—GRAEF J. R.—HENDERSON, J.: Implicit Fractional Differential and Integral Equations: Existence and Stability. De Gruyter, Berlin, 2018.10.1515/9783110553819 Search in Google Scholar

[3] ABBAS, S.—BENCHOHRA, M.—HAMIDI, N.: Successive approximations for the Darboux problem for implicit partial differential equations, PanAmer. Math. J. 28 (2018), no. 3, 1–10. Search in Google Scholar

[4] ABBAS, S.—BENCHOHRA, M.—N’GUÉRÉKATA, G. M.: Topics in Fractional Differential Equations, Springer-Verlag, Berlin, 2012.10.1007/978-1-4614-4036-9 Search in Google Scholar

[5] ABBAS, S.—BENCHOHRA, M.—N’GUÉRÉKATA, G. M.: Advanced Fractional Differential and Integral Equations. Nova Science Publishers, New York, 2015. Search in Google Scholar

[6] ABBAS, S.—BENCHOHRA, M.—NIETO, J. J. : Caputo-Fabrizio fractional differential equations with instantaneous impulses,AIMS Math. 6 (2021), 2932–2946.10.3934/math.2021177 Search in Google Scholar

[7] ATANACKOVIC, T. M.— PILIPOVIC, S.—STANKOVIC, B.—ZORICA, D.: Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes. Wiley-ISTE, London, Hoboken, 2014. Search in Google Scholar

[8] AYDOGAN, S.—BALEANU, D.—MOUSALOU, D.—REZAPOUR, S.: On approximate solutions for two higher order Caputo-Fabrizio fractional integro-differential equations, Adv. Difference Equ. 2017 (2017), art. no. 221, 1–11. Search in Google Scholar

[9] BALEANU, D.—MOUSALOU, A.—REZAPOUR, S.: On the existence of solutions for some infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential equations, Bound. Value Probl. 2017 (2017), art. no. 145, 1–9. Search in Google Scholar

[10] BASHIRI, T.—VAEZPOUR, M.—NIETO, J. J.: Approximating solution of Fabrizio-Caputo Volterra’s model for population growth in a closed system by homotopy analysis method, J. Funct. Spaces, 2018 (2018), https://doi.org/10.1155/2018/315250210.1155/2018/3152502 Search in Google Scholar

[11] BEKKOUCHE, M.—GUEBBAI, M.—KURULAY, H.—BENMAHMOUD, M.: A new fractional integral associated with the Caputo-Fabrizio fractional derivative, Rend. del Circolo Mat. di Palermo, Series II. (In Press); https://doi.org/10.1007/s12215-020-00557-810.1007/s12215-020-00557-8 Search in Google Scholar

[12] BROWDER, F.: On the convergence of successive approximations for nonlinear functional equations, Indag. Math. 30 (1968), 27–35.10.1016/S1385-7258(68)50004-0 Search in Google Scholar

[13] CAPUTO, M.—FABRIZIO, M.: A new definition of fractional derivative without singular kernel, Prog. Frac. Differ. Appl. 1 (2015), no. 2, 73–78. Search in Google Scholar

[14] CHEN, H. Y.: Successive approximations for solutions of functional integral equations, J. Math. Anal. Appl. 80 (1981), 19–30.10.1016/0022-247X(81)90087-1 Search in Google Scholar

[15] CZ LAPIŃSKI, T.: Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay, Opuscula Math. 34 (2014), no. 2, 327–338. Search in Google Scholar

[16] DOKUYUCU, M. A.: A fractional order alcoholism model via Caputo-Fabrizio derivative, AIMS Math. 5 (2020), 781–797.10.3934/math.2020053 Search in Google Scholar

[17] DOKUYUCU, M. A.—CELIK, E.—BULUT, H.—BASKONUS, H. M.: Cancer treatment model with the Caputo-Fabrizio fractional derivative,Eur.Phys. J. Plus 133 (2018), no. 3, 1–6. Search in Google Scholar

[18] FAINA, L.: The generic property of global convergence of successive approximations for functional differential equations with infinite delay, Commun. Appl. Anal. 3 (1999), 219–234. Search in Google Scholar

[19] FRUNZO, L.—GARRA, R.—GUSTI, A.—LUONGO, V.: Modeling biological system with an improved fractional Gompertz law, Comm. Nonlinear Sci. Numer. Simulat. 74 (2019), 260–267, https://doi.org/10.1016/j.cnsns.2019.03.02410.1016/j.cnsns.2019.03.024 Search in Google Scholar

[20] GAUL, L.—KLEIN, P.—KEMPFLE, S.: Damping description involving fractional operators, Mech. Syst. Signal Processing 5 (1991), 81–88.10.1016/0888-3270(91)90016-X Search in Google Scholar

[21] HILFER, R.: Applications of Fractional Calculus in Physics, World Scientific, Singapore, vii, 2000.10.1142/3779 Search in Google Scholar

[22] KILBAS, A. A.—SRIVASTAVA, H. M.—TRUJILLO, J. J.: Theory and Applications of Fractional Differential Equations. Elsevier Science B. V., Amsterdam, 2006. Search in Google Scholar

[23] LIU, Y.—FAN, E.—YIN, B.—LI, H.: Fast algorithm based on the novel approximation formula for the Caputo-Fabrizio fractional derivative.AIMS Math. 5 (2020), 1729–1744. Search in Google Scholar

[24] MAGIN, R. L.: Fractional calculus models of complex dynamics in biological tissues, Comput. Math. Appl. 59 (2010), no. 5, 1586–1593. Search in Google Scholar

[25] MAINARDI, F.: Fractional Calculus and Waves in Linear Viscoelasticity, an Introduction to Mathematical Model. Imperial College Press, World Scientific Publishing, London, 2010.10.1142/p614 Search in Google Scholar

[26] NIETO, J. J.: An abstract monotone iterative technique, Nonlinear Anal., Theory, Methods and Appl. 28 (1997), no. 12, 1923–1933. Search in Google Scholar

[27] SAMKO, S. G.—KILBAS, A. A.—MARICHEV, O. I.: Fractional Integrals and Derivatives Theory and Applications. Gordon and Breach, Amsterdam, 1987 (transl. from the Russian). Search in Google Scholar

[28] SHAIKH, A.—TASSADDIQ, A.—SOOPPY NISAR, K.—BALEANU, D.: Analysis of differential equations involving Caputo-Fabrizio fractional operator and its applications to reaction-diffusion equations, Adv. Difference Equ. 2019 (2019), art. no. 178, 1–14. Search in Google Scholar

[29] TARASOV, V. E. : Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media.In: Nonlinear Physical Science. Springer, Heidelberg; Higher Education Press, Beijing, 2010. Search in Google Scholar

[30] TOLEDO-HENRNANDEZ, R.— RICO-RAMIREZ, V.— IGLESIAS-SILVA, G. A.— DIWEKAR, U. M.: A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions,Chemical Engineering Science, 117 (2014), 217–228; http:dx.doi.org/10.1016/j.ces.2014.06.034 Search in Google Scholar

[31] TOLEDO-HENRNANDEZ, R.—RICO-RAMIREZ, V.— RICO-MARTINEZ, R.— HERNANDZO-CASTRO, S.—DIWEKAR, U. M.: A fractional calculus approach to the dynamic optimization of biological reactive systems. Part II: Numerical solution to fractional optimum control problems, Chemical Engineering Science, 117 (2014), 239–247; http://dx.doi.org/10.1016/j.ces.2014.06.033.8 Search in Google Scholar

[32] ZHOU, Y.—WANG, J. R.— ZHANG, L.: Basic Theory of Fractional Differential Equations (2nd edition). World Scientific Publishing Co. Pte. Ltd., Hackensack, N. J., 2017.10.1142/10238 Search in Google Scholar

eISSN:
1338-9750
Język:
Angielski
Częstotliwość wydawania:
3 razy w roku
Dziedziny czasopisma:
Mathematics, General Mathematics