AN ANALYTICAL APPROACH OF THE WRONSKIAN METHOD FOR THE DISCUSSION OF THE SOLUTION OF CONFORMABLE FRACTIONAL DIFFERENTIAL EQUATIONS

Abstract

In this work, we introduce a method Wronskian for solving fractional differential equations with fractional derivatives defined by the conformable fractional derivatives. For illustrating the linear dependent or independent solution of fractional differential equations we use the Wronskian method. One of the greatest advantages of the wronskian is that it can be used with higher order differential equations, and so, for any nth order differential equation, as long as you know  solutions, the wronskian aids in solving for the last general solution while adding information on the rest of them, such as linear  To test the efficiency of this approach some illustrative examples are presented for verifying whether the solution of a FDE is linearly dependent or independent. Moreover, some properties of fractional Wronskian are discussed. In the non-homogeneous case, we present the Wronskian method to verify the solution of FDE.