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چکیده
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Numerous researchers and mathematicians have exhibited fractional derivative and integral operators as powerful tools to describe and model many phenomena in various branches of science such as signal processing, medicine, economics, dynamics of viscoelastic materials, colored noise, bioengineering, continuum and statistical mechanics, biology, earthquake, electromagnetism, electrochemistry, solid mechanics, fluid-dynamic traffic model, and seepage flow in porous media [1–9]. Several definitions of fractional derivatives have been presented including the Riemann–Liouville [2], Caputo [3], Riesz [10], and Riesz–Feller [10] definitions. Many researches have been used to solve fractional differential equations (FDEs), fractional integro-differential equations (FIDEs), and fractional partial differential equations (FPDEs). Heydari et al. [11] used the orthonormal piecewise Vieta–Lucas functions for solving the piecewise fractional Galilei invariant advection–diffusion equations. Zhou and Xu [12] proposed the third-kind Chebyshev wavelet collocation method for solving the time-fractional convection diffusion equations with variable coefficients. The authors of [13] introduced fractional Chebyshev cardinal wavelets for numerical solution of fractional quadratic integro-differential equations. The authors of [14] proposed the two-dimensional Müntz–Legendre hybrid function method to solve fractional-order partial differential equations. Rahimkhani and Ordokhani [15] solved fractional variational and optimal control problems by using Bernstein wavelets method; they [16] also used the bivariate Müntz wavelet composite collocation method for solving FPDEs. Sabermahani et al. [17] developed the Fibonacci wavelet method for approximate solution of FPDEs arising in the financial markets
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