An effective sustainable collocation method for solving regular/singular systems of conformable differential equations subject to initial constraint conditions

The main objective of the present article is to provide an overview of the B-splines collocation methods (BSCM) to achieve practical analytical-numerical solutions for a family of regular/singular systems of initial con-straints condition (ICC). Herein, the fractional derivatives are described by the conformable one, and an abundance of its basic theory is utilized. The useful properties of the cubic B-splines and collocation methods are employed to reduce the computations of both regular/singular systems of fractional or-der to a combination of linear/nonlinear algebraic equations. Numerical tests are treated quantitatively to demonstrate the technical statements and to ex-hibit the ability, perfection, and applicability of the suggested procedure for solving such conformable systems models. The outcomes confirm the relia-bility and efficacy of the technique improved. At the end of the manuscript, some notes were presented with some characteristics of the scheme and some possible future work.