The construction of operational matrix of fractional derivatives using B-spline functions

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper.

► In the current paper the fractional differential equations are investigated.
► A numerical technique based on linear B-Spline functions is presented to find its solution.
► Also the method is based on constructing the operational matrix of fractional derivative.
► Thus the main problem is reduced to problem of solving a system of algebraic equations.
► The method is tested on several examples of various types to show its validity.