Approximate solution for high-order fractional integro-differential equations via trigonometric basic functions

Abstract

An approach for searching an approximate solution of high-order integro-differential equations featuring fractional derivatives has been proposed in this paper. Initially, using trigonometric basic functions (TBFs), we determine the transformation functions in association to TBFs. Next, the approximate function is presented as a combination of TBFs and transform functions. The convergence of this approach is also presented. Using discrete derivatives of the solution to gain an approximate solution, we find the approximate solution, which satisfies the high-order integro-differential equations featuring fractional derivatives. An algorithm of this approach is applied for various examples, and one example is illustrated in detail.