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.
 V. Balachandran and K. Murugesan, Analysis of electronic circuits using the single-Term Walsh series approach,
Int. J. Elect. 69 (1990) 327–322.
 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.
 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.
 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.
 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.
 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.
 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
 W. Deng, C. Li C and Q. Guo , Analysis of fractional differential equations with multi-orders Fract. 15 (2007)
 R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: a fractional dynamics approach,
Phys. Rep. 339 (2000) 1–77.
 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.
 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.
 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.
 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.
 X. Li and C. Xu, A space–time spectral method for the time fractional diffusion equation, SIAM J. Numer. Anal.
47 (2009) 2108–2131.
 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.
 A.A. Khajehnasiri and M. Safavi. Solving fractional Black-Scholes equation by using Boubaker functions, Math.
Meth. Appl. Sci. 39 (2021) 1–11. F. Liu, V. Anh and I. Turner, Numerical solution of the space fractional Fokker-Planck equation, J. Comput.
Appl. Math. 166 (2004) 209–219.
 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.
 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.
 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.
 I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
 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.
 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.
 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.
 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.
 A. Saadatmandi and M. Dehghan, A new operational matrix for solving fractional-order differential equations,
Comput. Math. Appl, 59 (2010) 1326–1336.
 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.
 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.
 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.
 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.
 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.