Numerical Solution of Multi-Order Fractional Differential Equations Using Generalized Sine-Cosine Wavelets

In this work, we propose a numerical method based on the generalized sine-cosine wavelets for solving multi-order fractional differential equations. After introducing generalized sine-cosine wavelets, the operational matrix of Riemann-Liouville fractional integration is constructed using the properties of the block-pulse functions. The fractional derivative in the problem is considered in the Caputo sense. This method reduces the considered problem to the problem of solving a system of nonlinear algebraic equations. Finally, some examples are included to demonstrate the applicability of the new approach.

Keywords:

Generalized sine-cosine wavelet, Operational matrix of fractional integration, Multi-order fractional differential equations Block-pulse functions, Operational matrix of fractional integration,

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