The B-spline collocation method for solving conformable initial value problems of non-singular and singular types

Abstract

In the present study, the uniform cubic B-spline collocation method is constructed, employed, and experimented to given smooth approximations for the numerical solution of a class of linear and nonlinear fractional initial value problems of singular and non-singular types based on the conformable fractional derivative. As a special case, the singular Lane-Emden type model is presented such that the source fractional differential equation is transformed at the point of singularity. The converted issue is then solved by using third B-splines on a uniform mesh approximation procedure with help of Mathematica 11. Several illustrative examples are incorporated to demonstrate the efficiency, validity, and applicability of the proposed technique for such conformable problems.

Keywords

• Fractional differential equation
• B-spline collocation method
• Conformable derivative
• Initial value problem
• Lane-Emden type model