### Numerical Solution for A Class of Fractional Variational Problem via Second Order B-Spline Function

Noratiqah Farhana binti Ismail, Chang Phang

#### Abstract

In this paper, we solve a class of fractional variational problems (FVPs) by using operational matrix of fractional integration which derived from second order spline (B-spline) basis function. The fractional derivative is defined in the Caputo and Riemann-Liouville fractional integral operator. The B-spline function with unknown coefficients and B-spline operational matrix of integration are used to replace the fractional derivative which is in the performance index. Next, we applied the method of constrained extremum which involved a set of Lagrange multipliers. As a result, we get a system of algebraic equations which can be solve easily. Hence, the value for unknown coefficients of B-spline function is obtained as well as the solution for the FVPs. Finally, the illustrative examples shown the validity and applicability of this method to solve FVPs.

#### Keywords

fractional variational problems; B-spline function; operational matrix of integration; Riemann-Liouville fractional integration; Lagrange multiplier

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DOI: https://doi.org/10.22342/jims.25.3.672.171-182

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