New Spectral Solutions of Multi-Term Fractional-Order Initial Value ProblemsWith Error Analysis
W. M. Abd-Elhameed and Y. H. Youssri

doi:10.3970/cmes.2015.105.375
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 105, No. 5, pp. 375-398, 2015
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Keywords Wavelets, ultraspherical polynomials, collocation method, fractionalorder differential equations
Abstract

In this paper, a new spectral algorithm for solving linear and nonlinear fractional-order initial value problems is established. The key idea for obtaining the suggested spectral numerical solutions for these equations is actually based on utilizing the ultraspherical wavelets along with applying the collocation method to reduce the fractional differential equation with its initial conditions into a system of linear or nonlinear algebraic equations in the unknown expansion coefficients. The convergence and error analysis of the suggested ultraspherical wavelets expansion are carefully discussed. For the sake of testing the proposed algorithm, some numerical examples are considered. The numerical results indicate that the resulting approximate solutions are close to the analytical solutions and they are more accurate than those obtained by some other existing techniques in literature.

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