An inverse problem approach to determine possible memory length of fractional differential equations

References

[1] R.P. Agarwal, M. Benchohra, S. Hamani, A survey on existence results for boundary value problems of nonlinear fractional differential equations and inclusions. Acta Appl. Math. 109, No 3 (2010), 973–1033.10.1007/s10440-008-9356-6Search in Google Scholar

[2] M. Al–Refai, M.A. Hajji, Monotone iterative sequences for nonlinear boundary value problems of fractional order. Nonlinear Anal.: Theor. Method. Appl. 74, No 11 (2011), 3531–3539.10.1016/j.na.2011.03.006Search in Google Scholar

[3] A. Granas, J. Dugundji, Fixed Point Theory. Springer, New York (2003).10.1007/978-0-387-21593-8Search in Google Scholar

[4] [4]L.L. Huang, J.H. Park, G.C. Wu, Z.W. Mo, Variable–order fractional discrete–time recurrent neural networks. J. Comput. Appl. Math. 370 (2020), # 112633.10.1016/j.cam.2019.112633Search in Google Scholar

[5] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North–Holland Math. Studies, 204, Elsevier, Amsterdam (2006).Search in Google Scholar

[6] A. Liemert, A. Kienle, Fundamental solution of the tempered fractional diffusion equation. J. Math. Phys. 56, No 11 (2015), # 113504.10.1063/1.4935475Search in Google Scholar

[7] C. Li, W.H. Deng, L.J. Zhao, Well–posedness and numerical algorithm for the tempered fractional ordinary differential equations, Discrete Contin. Dyn. Syst. Ser. B 24, No 4 (2019), 1989–2015.Search in Google Scholar

[8] Y. Li, Y.Q. Chen, I. Podlubny, Stability of fractional–order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput. Math. Appl. 59, No 5 (2010), 1810–1821.10.1016/j.camwa.2009.08.019Search in Google Scholar

[9] M.L. Morgado, M. Rebelo, Well-posedness and numerical approximation of tempered fractional terminal value problems. Fract. Calc. Appl. Anal. 20, No 5 (2017), 1239–1262; 10.1515/fca-2017-0065; https://www.degruyter.com/journal/key/fca/20/5/html.Search in Google Scholar

[10] M.M. Meerschaert, Y. Zhang, B. Baeumer, Tempered anomalous diffusion in heterogeneous systems. Geophys. Resear. Lett. 35, No 17 (2008), # L17403.10.1029/2008GL034899Search in Google Scholar

[11] I. Podlubny, Fractional Differential Equations. Academic Press, San Diego (1999).Search in Google Scholar

[12] B. Shiri, G.C. Wu, D. Baleanu, Collocation methods for terminal value problems of tempered fractional differential equations. Appl Numer. Math. 156 (2020), 385–395.10.1016/j.apnum.2020.05.007Search in Google Scholar

[13] D.R. Smart, Fixed Point Theorems. Cambridge University Press, Cambridge (1980).Search in Google Scholar

[14] F. Sabzikar, M.M. Meerschaert, J. Chen, Tempered fractional calculus. J. Comput. Phys. 93 (2015), 14–28.10.1016/j.jcp.2014.04.024Search in Google Scholar PubMed PubMed Central

[15] V.V. Tarasova, V.E. Tarasov, Economic interpretation of fractional derivative. Progr. Fract. Differ. Appl. 1 (2017), 1–7.10.18576/pfda/030101Search in Google Scholar

[16] G.C. Wu, M. Luo, L.L. Huang, S. Banerjee, Short memory fractional differential equations for new memristor and neural network design. Nonlinear Dyna. 100, No 4 (2020), 3611–3623.10.1007/s11071-020-05572-zSearch in Google Scholar

[17] G.C. Wu, D.Q. Zeng, D. Baleanu, Fractional impulsive differential equations: exact solutions, integral equations and short memory case. Fract. Calc. Appl. Anal. 22, No 1 (2019), 180–192; 10.1515/fca-2019-0012; https://www.degruyter.com/journal/key/fca/22/1/html.Search in Google Scholar

[18] S.Q. Zhang, Existence of solution for a boundary value problem of fractional order. Acta Math. Sci. 26, No 2 (2006), 220–228.10.1016/S0252-9602(06)60044-1Search in Google Scholar