What is it about?

we consider a new fractional function based on Legendre and Laguerre poly- nomials for solving a class of linear and nonlinear time-space fractional partial differential equations with variable coefficients. The concept of the fractional derivative is utilized in the Caputo sense. The idea of solving these problems is based on operational and pseudo- operational matrices of integer and fractional order integration with the collocation method.

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Why is it important?

In this paper, we have introduced a fractional function based on Legendre and Laguerre polynomials and applied it to the numerical solution of fractional partial differential equations. In order to solve this type of problem, we used the collocation method and integral operational and pseudo-operational matrix with integer and fractional order.

Perspectives

Writing this article was a great pleasure as it has co-authors with whom I have had long-standing collaborations. Also, this article also leads to greater involvement with other researchers in this subject area.

Dr. Haniye Dehestani
Alzahra University

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This page is a summary of: Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations, Applied Mathematics and Computation, November 2018, Elsevier, DOI: 10.1016/j.amc.2018.05.017.
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