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**A new operational matrix of fractional derivatives to solve systems of fractional differential equations via Legendre wavelets.**
*(English)*
Zbl 1417.65146

With the effectiveness and correctness, and comparing the approach involved in the paper with other existing methods, this paper demonstrates the advantage of employing the Legendre wavelet operational matrix method. This understanding and the claim is justified through numerical analysis of fractional-order differential equations using the method used in the paper. Among other advantages, the proposed method describes a comprehensible approach to reduce fractional differential equations and the system of such equations to a system of algebraic equations. Section 5, through illustrative examples, explains the numerical approach in attaining the success of the method employed in the paper. Liouville-Caputo fractional-order derivative, shifted Legendre polynomials, and the Legendre wavelets involve in the investigation. This paper, as that appears, is the outcome of a paper [A. Saadatmandi and M. Dehghan, Comput. Math. Appl. 59, No. 3, 1326–1336 (2010; Zbl 1189.65151)], in which the operational matrix of a fractional derivative is obtained by invoking shifted Legendre polynomials. An effective operational algorithm is used to obtain the solution of the linear and non-linear system of fractional differential equations in Maple. The authors of the present paper propagate a potential use of the method used in their investigation for solving fractional partial differential equations, fractional integral equations, and a system of such.

Reviewer: Deshna Loonker (Jodhpur)

### MSC:

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

34A08 | Fractional ordinary differential equations |

65T60 | Numerical methods for wavelets |

### Citations:

Zbl 1189.65151### Software:

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\textit{A. Secer} and \textit{S. Altun}, Mathematics 6, No. 11, Paper No. 238, 16 p. (2018; Zbl 1417.65146)

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### References:

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