Generalized hat functions method for solving fractional integro-differential equations of bratu-type

In this paper, a numerical scheme, based on fractional order generalized hat functions operational matrix of integration for solving fractional integro-differential equations of Bratu-type is presented. The operational matrix is used to reduce the fractional integro-differential equation to a system of algebraic equations. The error analysis of generalized hat functions is also given. Numerical examples are provided to demonstrate the validity and applicability of the method. Moreover, comparing the methodology with the known technique shows that our approach is more efficient and more accurate.