Convergence Analysis of Cubic Spline Function with Fractional Degree and Applications

In this paper, a fractional degree cubic spline scheme is proposed and analyzed for order with the multi-term Riemann–Liouvile (R–L) derivatives. For integral differential equations, we handle continuity equations attain system of linear algebraic by using matrix method based on piecewise test functions. The to solve initial value problems approximate solution equation approximation Reimann–Liouvile derivative. obtain fully discrete method, standard used spatial derivative conditions that suitable provided model unique exist all interval which are appeared in function derivatives order. convergence analysis rigorously proved method. addition, existence uniqueness numerical solutions systems strictly. Numerical results confirm theoretical show effectiveness