A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented and compared with the results in literature, which reveals wonderful results.
Abdelkawy, M. A.
Accurate Spectral Algorithms for Solving Variable-order Fractional Percolation Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 15,
2, Article 18.
Available at: https://digitalcommons.pvamu.edu/aam/vol15/iss2/18