Spline Collocation Method for Nonlinear Multi-Term Fractional Differential Equation

TL;DR

This paper introduces a spline collocation method to numerically solve nonlinear multi-term fractional differential equations, providing proofs of existence, uniqueness, convergence, and error estimates for the solutions.

Contribution

The paper develops a novel spline collocation approach for nonlinear multi-term fractional differential equations, including theoretical analysis and error bounds.

Findings

Proves existence and uniqueness of solutions.

Establishes convergence and error estimates.

Provides a practical approximation method for complex equations.

Abstract

We study an approximation method to solve nonlinear multi-term fractional differential equations with initial conditions or boundary conditions. First, we transform the nonlinear multi-term fractional differential equations with initial conditions and boundary conditions to nonlinear fractional integral equations and consider the relations between them. We present a Spline Collocation Method and prove the existence, uniqueness and convergence of approximate solution as well as error estimation. The approximate solution of fractional differential equation is obtained by fractional integration of the approximate solution for fractional integral equation.