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.1.1.672.1-12

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