We propose a new type of non-polynomial fractional spline function with fractional continuity conditions for integral equations. The Caputo fractional derivative was used to generate fractional spline derivatives. Moreover, the convergence analysis was investigated. The approach is also well discussed and supported with computational numerical results, with the results indicating that it is both accurate and simple to implement.

To compute the solution of FDEs, we create a fractional polynomial spline in this paper; the spline interpolation with fractional polynomial coefficients must be constructed using the Caputo fractional derivative. Error bounds were studied and a stability analysis was completed for the given spline function. Four examples were used to consider the numerical explanation for the provided method. The research suggests that the fractional spline function, which interpolates data, is useful and accurate in solving unique problems.