An efficient method for solving fractional integral and differential equations of Bratu type

Abstract

In this paper, the fractional integral and differential equations of Bratu type, which arise in many important physical phenomena, are investigated by an effective technique, Chebyshev Finite Difference Method with the help of fractional derivative in the concept of Caputo. The effect of the fractional derivative in the outcomes has great agreement with the nonlocality of the problem. The truncation and round off errors and convergence analyzes of the present method are also given. Numerical solutions of illustrative examples of the fractional integral and differential equations of Bratu type are given to highlight the validity and performance of the method. The results of the comparisons are very satisfied and show that the proposed technique is more effective and highly accurate than the other methods.