A NUMERICAL APPROACH FOR SOLVING FRACTIONAL LINEAR BOUNDARY VALUE PROBLEMS USING SHOOTING METHOD

This paper is devoted to introducing a novel numerical approach for approximating solutions to Fractional Linear Boundary Value Problems (FLBVPs). Such an approach will be carried out by using a new fractional version of the shooting method, which would convert the FLBVP into a linear system of two fractional initial value problems. This system can then be solved by the so-called fractional Euler method. The numerical solution of the main FLBVP will ultimately be a linear combination of the solutions of the two equations of the fractional-order system. A number of illustrative examples will be presented in order to confirm that the suggested numerical technique is valid.