[1] I. Aziza, S. ul-Islam and F. Khan, A new method based on Haar wavelet for the numerical solution of twodimensional nonlinear integral equations, J. Comput. Appl. Math. 272 (2014) 70–80.
[2] V. Balachandran and K. Murugesan, Analysis of electronic circuits using the single-Term Walsh series approach,
Int. J. Elect. 69 (1990) 327–322.
[3] V. Balakumar and K. Murugesan, Single-Term Walsh series method for systems of linear volterra integral equations of the second kind, Appl. Math. Comput. 228 (2014) 371–376.
[4] A.H. Bhrawy, E.H. Doha, D. Baleanu and S. Ezz-Eldien, A spectral tau algorithm based on Jacobi operational
matrix for numerical solution of time fractional diffusion-wave equations, 293 (2015) 142–156.
[5] R. Chandra Guru Sekar, K. Murugesan, Single Term Walsh Series Method for system of nonlinear delay volterra
integro-differential equations describing biological species living together, Int. J. Appl. Comput. Comput. Math.
42 (2018) 1–13.
[6] R. Chandra Guru Sekar, K. Murugesan, Numerical solutions of nonlinear system of higher order volterra integrodifferential equations using generalized STWS technique, Diff. Equ. Dyn. Syst. 60 (2017) 1–13.
[7] R. Chandra Guru Sekar and K. Murugesan, System of linear second order volterra integro-differential equation
using single term Walsh series technique, Appl. Math. Comput. 273 (2016) 484–492.
[8] J. Chen, F. Liu, V. Anh, S. Shen, Q. Liu and C. Liao, The analytical solution and numerical solution of the
fractional diffusion-wave equation with damping, Appl. Math. Comput. 219 (2012) 1737–1748
[9] W. Deng, C. Li C and Q. Guo , Analysis of fractional differential equations with multi-orders Fract. 15 (2007)
173–182.
[10] R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach,
Phys. Rep. 339 (2000) 1–77.
[11] E.H. Doha, A.H. Bhrawy and S.S. Ezz-Eldien, A Chebyshev spectral method based on operational matrix for initial
and boundary value problems of fractional order, Comput. Math. Appl. 62 (2011) 2364–2373.
[12] A. Ebadian and A.A. Khajehnasiri, Block-pulse functions and their applications to solving systems of higher-order
nonlinear Volterra integro-differential equations, Elect. J. Diff. Equ. 54 (2014) 1–9.
[13] M. H. Heydri, M. R. Hooshmandasl, F. M. Maalek Ghaini and C. Cattani, Wavelets method for the time fractional
diffusion-wave equation, Phys. Lett. A 379 (2015) 71–76.
[14] A.A. Khajehnasiri, Numerical Solution of Nonlinear 2D Volterra-Fredholm Integro-Differential Equations by TwoDimensional Triangular Function, Int. J. Appl. Comput. Math. 2 (2016) 575–591.
[15] X. Li and C. Xu, A space–time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal.
47 (2009) 2108–2131.
[16] A.A. Khajehnasiri, R. Ezzati and M. Afshar Kermani. Solving fractional two-dimensional nonlinear partial
Volterra integral equation by using bernoulli wavelet, Iran J. Sci. Tech. Trans. Sci. (2021) 1-13.
[17] A.A. Khajehnasiri and M. Safavi. Solving fractional Black-Scholes equation by using Boubaker functions, Math.
Meth. Appl. Sci. 39 (2021) 1–11.[18] F. Liu, V. Anh and I. Turner, Numerical solution of the space fractional Fokker-Planck equation, J. Comput.
Appl. Math. 166 (2004) 209–219.
[19] F. Liu, M.M. Meerschaert, R.J. McGough, P. Zhuang and Q. Liu, Numerical methods for solving the multi-term
time-fractional wave-diffusion equation, Fract. Calc. Appl. Anal. 16 (2013) 9–25.
[20] F. Mainardi, M. Raberto, R. Gorenflo and E. Scalas, Fractional calculus and continuous-time finance II: the
waiting-time distribution, Phys. A. 287 (2000) 468–481.
[21] R. Metler and J. Klafter, The restaurant at the end of random walk: recent developments in the description of
anomalous transport by fractional dynamics, J. Phys. A 37 (2004) 161–208.
[22] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
[23] H. Rahmani Fazli, F. Hassani, A. Ebadian and A.A. Khajehnasiri. National economies in state-space of fractionalorder financial system, Afrika Mat. 27 (2016) 529–540.
[24] G.P. Rao, K.R. Palanisamy and T. Srinirasan, Extension of computation beyond the limit of initial normal interval
in Walsh series analysis of dynamical systems, IEEE Trans. Autom. Cont. 25 (1980) 317–319.
[25] S.Yu. Reutskiy, A new semi-analytical collocation method for solving multi-term fractional partial differential
equations with time variable coefficients, Appl. Math. Model. 45 (2017) 238–254.
[26] M. Raberto, E. Scalas and F. Mainardi, Waiting-times and return in high-frequency financial data: an empirical
study, Phys. A. 314 (2002) 749–755.
[27] A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional-order differential equations,
Comput. Math. Appl, 59 (2010) 1326–1336.
[28] S. Shen, F. Liu, V. Anh and I. Turner, The fundamental solution and numerical solution of the Riesz fractional
advection-dispersion equation, IMA J. Appl. Math. 73 (2008) 850–872.
[29] Z. Wang and S. Vong, Compact difference schemes for the modified anomalous fractional sub-diffusion equation
and the fractional diffusion-wave equation, J. Comput. Phys. 277 (2014) 1–15.
[30] Y. Yang, Y. Chen,Y. Huang and H. Wei, Spectral collocation method for the time-fractional diffusion-wave equation
and convergence analysis, Comput. Math. Appl. 73 (2017) 1218–1232.
[31] W. Zhanga, J. Lia and Y. Yang, A fractional diffusion-wave equation with non-local regularization for image
denoising, Signal Process. 103 (2014) 6–15.
[32] M. Zheng, F. Liu, V. Anh and I. Turner, A high order spectral method for the multi-term time-fractional diffusion
equations, Appl. Math. Model. 40 (2016) 970–985.