1. Doha E. H., Bhrawy A. H., Ezz-Eldien S. S., "An efficient Legendre spectral tau matrix formulation for solving fractional subdiffusion and reaction subdiffusion equations", J. Comput. Nonlinear Dyn 10 (2) 021019 (2015) 1-021018. ## 2. Garg M., Manohar P., "Matrix method for numerical solution of space-time fractional diffusion-wave equations with three space variables", Afr. Mat. 25 (1) (2014) 161-181. ## 3. Karimi Vanani S., Aminataei A., "On the numerical solution of neutral delay differential equations using multiquadric approximation scheme, Bull. Korean Math. Soc., 45, (2008 663-670. ## 4. Laskin N., "Fractional quantum mechanics", Phys. Rev. E., 62, (2003) 3135-3145. ## 5. Kreyszig E., "Introductory Functional Analysis with Applications", John Wiley and Sons, New York, NY, USA (1978). ## 6. Krishnasamy V.S., Mashayekhi S., Razzaghi M., "Numerical solutions of fractional differential equations by using fractional Taylor basis", IEEE/CAA Journal of Automatica Sinica, 4 (1) (2017) 98-106. ## 7. Li Y., Zhao W., "Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations", Appl. Math. Comput. 216, (2010) 2276-2285. ## 8. Mashayekhi S., Razzaghi M., Wattanataweekul M., "Analysis of multi-delay and piecewise constant delay systems by hybrid functions approximation", Differential Equations and Dynamical Systems. 24, (1) (2016) 1-24. ## 9. Moghaddam B. P., Mostaghim Z. S., "A matrix scheme based on fractional finite difference method for solving fractional delay differential equations with boundary conditions", New Trends in Mathematical Sciences,2, (2015) 13-23. ## 10. Moghaddam B. P., Mostaghim Z.S., "A novel matrix approach to fractional finite difference for solving models based on nonlinear fractional delay differential equations", Ain Shams Engineering Journal 5, (2014) 585-594. ## 11. Moghaddam B. P., Mostaghim Z. S., "A numerical method based on finite difference for solving fractional delay differential equations", J. Taibah. Univ. Sci., 7, (2013) 120-127. ## 12. Ordokhani Y., "An Application of Walsh functions for Fredholm-Hammerstein integro-differential equations, Int. J. Contemp. Math. Sciences 5 (22) (2010) 1055-1063. ## 13.. Ordokhani Y., "Solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via rationalized Haar functions", Appl. Math. Comput, 180, (2006) 436-443. ## 14. Petras I., "Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation", Higher Education Press, Beijing (2011). ## 15. Pimenov V. G., Hendy A. S., "Numerical studies for fractional functional differential equations with delay based on BDF-Type shifted chebyshev approximations", Abstract and Applied Analysis (2015) 1-12. ## 16. Rahimkhani P., Ordokhani Y., Babolian E., "A new operational matrix based on Bernoulli wavelets for solving fractional delay differential equations", Numer. Algor, 74 (1) (2017) 223-245. ## 17. Rahimkhani P., Ordokhani Y., Babolian E., "Fractional-order Bernoulli functions and their applications in solving fractional Fredholem-Volterra integro-differential equations", Appl. Numer. Math., 122 (2017) 66-81. ## 18. Rahimkhani P., Ordokhani Y., Babolian E., "Fractional-order Bernoulli wavelets and their applications", Appl. Math. Model., 40 (2016) 8087-8107. ## 19. Rahimkhani P., Ordokhani Y., Babolian E., "Muntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations", Numer. Algor., 77 (4) (2018) 1283-1305. ## 20. Rahmani Fazli H., Hassani F., Ebadian A., Khajehnasiri A. A., "National economies in state-space of fractional-order financial system", Afr. Mat., 27 (3-4) (2016) 529-540. ## 21. Saeed U., Rehman M., "Modified Chebyshev wavelet methods for fractional delay-type equations", Appl. Math. Comput, 264 (2015) 431-442. ## 22. Saichev A. I., Zaslavsky G. M., "Fractional kinetic equations: solutions and applications", Chaos 7, (1997) 753-764. ## 23. Samiei E., Butcher E. A., Sanyal A. K., Paz R., "Attitude stabilization of rigid spacecraft with minimal attitude coordinates and unknown time-varying delay", Aerospace Science and Technology, 46 (2015) 412-421. ## 24. Segalman D. J., Butcher E. A., "Suppression of regenerative chatter via impedance modulation", J. Vib. Control 6, (2000) 243-256. ## 25. Tarasov V. E., "Fractional variations for dynamical systems: Hamilton and Lagrange approaches", J. Phys. A. Math. Gen. 39 (2006) 8409-8425. ## 26. Wang Z., "A numerical method for delayed fractional-order differential equations", J. Appl. Math., (2013) 1-7. ## 27. Wang H., Du N., "Fast alternating-direction finite difference methods for three dimensional space-fractional diffusion equations", J. Comput. Phys. 258 (2014) 305-318. ## 28. Xiea W., Xiaob J., Luo Z., "Existence of extremal solutions for nonlinear fractional differential equation with nonlinear boundary conditions", Appl. Math. Lette. 41 (2015) 46-51. ## 29. Yang Z., Cao J., "Initial value problems for arbitrary order fractional differential equations with delay", Communications in Nonlinear Science and Numerical Simulation, 18 (2013) 2993-3005. ## 30. Yang X., Zhang H., Xu D., "Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation", J. Comput. Phys. 256 (2014) 824-837. ## 31. Zhu L., Fan Q., "Solving fractional nonlinear Fredholm integro-differential equations by the second kind Chebyshev wavelet", Commun. Nonlinear Sci. Numer. Simulat, 17 (2012) 2333-2341. ## 32. Zhuang P., Liu F., Turner I., Gu Y. T., "Finite volume and finite element methods for solving a one-dimensional space-fractional Boussinesq equation", Appl. Math. Model, 38 (2014) 3860-3870. ##