Fuzzy transform based approximation method for solving fractional semi-explicit differential-algebraic equations

Abstract

We present an efficient numerical method to approximate the solution of a system of fractional-order linear semi-explicit differential-algebraic equations with variable coefficients. The method is based on the use of the direct and inverse fuzzy transforms (F-transforms). By employing this method, we obtain an analytical approximate solution to the main problem in terms of flexible basic functions. The nonlocal property of fuzzy transforms helps us to have an efficient method for problems involving non-singular kernels. The error analysis and convergence evaluation of the method is demonstrated in detail. We give some examples to illustrate the significant features of the method.