References
- D. Baleanu, K. Diethelm, E. Scalas, and J.J. Trujillo, Fractional Calculus Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, World Scientific, Boston, 2012.
- B. Bandyopadhyay and S. Kamal, Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach, Vol. 317, Springer International Publishing, Switzerland, 2015.
- J. Cao and C. Xu. A high order schema for the numerical solution of the fractional ordinary differential equations, J. Comput. Phys. 238 (2013), pp. 154–168. doi: 10.1016/j.jcp.2012.12.013
- Y.M. Chen, Theorems of asymptotic approximation, Math. Ann. 140 (1960), pp. 360–407. doi: 10.1007/BF01361220
- J. Dascioglu and H. Yaslan, The solution of high-order nonlinear ordinary differential Eqs, Appl. Math. Comput. 217 (2011), pp. 5658–5666.
- W. Deng, Sh. Du, and Y. Wu, High order finite difference WENO schemes for fractional differential equations, Appl. Math. Lett. 26 (2013), pp. 362–366. doi: 10.1016/j.aml.2012.10.005
- R. Fuller, Neural Fuzzy Systems, Abo Akademi University Press, Budapest, 2005.
- D. Graupe, Principles of Artificial Neural Networks, 2nd ed., World Scientific Publishing, Chicago, 2007.
- M. Hanss, Applied Fuzzy Arithmetic: An Introduction with Engineering Applications, Springer-Verlag, Berlin, 2005.
- M.H. Hassoun, Fundamentals of Artificial Neural Networks, MIT Press, Cambridge, MA, 1995.
- R.A. Jacobs, Increased rates of convergence through learning rate adaptation, Neural Netw. 1 (1988), pp. 295–307. doi: 10.1016/0893-6080(88)90003-2
- A. Jafarian, F. Rostami, A.K. Golmankhaneh, and D. Baleanu, Using ANNs approach for solving fractional order Volterra integro-differential equations, Int J Comput Int Sys. 10 (2017), pp. 470–480. doi: 10.2991/ijcis.2017.10.1.32
- Y. Keskyn, O Karaodlu, S. Servy, and G. Oturanc, The approximate solution of high-order linear fractional differential equations with variable coefficients in terms of generalized Taylor polynomials, Math. Comput. Appl. 16(3) (2011), pp. 617–629.
- M.M. Khader, T.S. El-Danaf, and A.S. Hendy, A computational matrix method for solving systems of high order fractional differential equations, Appl. Math. Model. 37 (2013), pp. 4035–4050. doi: 10.1016/j.apm.2012.08.009
- G.S. Ladde, V. Lakashmkautham, and B.G. Zhang, Oscillation Theory of Differential Equations with Deviating Arguments, Dekker, New York, 1987.
- V. Lakshmikantham, S. Leela, and J. Vasundhara Devi, Theory of Fractional Dynamic Systems, Cambridge University Press, Cambridge, 2009.
- S. Momani and Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons Fractals 31(5) (2007), pp. 1248–1255. doi: 10.1016/j.chaos.2005.10.068
- M. Muslim, Existence and approximation of solutions to fractional differential equations, Math. Comput. Modelling 49 (2009), pp. 1164–1172. doi: 10.1016/j.mcm.2008.07.013
- I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
- R. Rojas, Neural Networks, Systematic Introduction, Springer-Verlag, Berlin, 1996.
- X.J. Yang, Advanced Local Fractional Calculus and its Applications, World Science Publisher, New York, 2012.
- X. Zhang, L. Liu, and Y. Wu, The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives, Appl. Math. Comput. 218 (2012), pp. 8526–8536.