A new and efficient approach for solving linear and nonlinear time-fractional diffusion equations of distributed order. (English) Zbl 1524.35689
Summary: This paper is concerned with a computational approach based on the Jacobi wavelets for linear and nonlinear time-fractional diffusion equations of distributed order. We derive the Jacobi wavelet operational vector for the Riemann-Liouville fractional integral operator. By applying this operational vector via the Gauss-Legendre quadrature formula and collocation method in our approach, the problems can be reduced to systems of linear or nonlinear algebraic equations which can be solved by the Newton method. The convergence and some error bounds of the expressed method are theoretically investigated. In addition, the presented method is implemented for six test problems. Comparisons between the obtained numerical results and other methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.
MSC:
| 35R11 | Fractional partial differential equations |
| 26A33 | Fractional derivatives and integrals |
| 65T60 | Numerical methods for wavelets |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
Keywords:
distributed-order fractional derivative; diffusion equations; operational vector; Jacobi wavelets; error boundsReferences:
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