Legendre wavelets approach for numerical solutions of distributed order fractional differential equations

By Boonrod Yuttanan, Mohsen Razzaghi. Applied Mathematical Modelling, 2019

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Abstract In this study, a new numerical method for the solution of the linear and nonlinear distributed fractional differential equations is introduced. The fractional derivative is described in the Caputo sense. The suggested framework is based upon Legendre wavelets approximations. For the first time, an exact formula for the Riemann–Liouville fractional integral operator for the Legendre wavelets is derived. We then use this formula and the properties of Legendre wavelets to reduce the given problem into a system of algebraic equations. Several illustrative examples are included to observe the validity, effectiveness and accuracy of the present numerical method.

Subfields: Applied Mathematics, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0912fb5559e6f2c2022b023c874ba48500fa7e7e