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 ( $${\mathcal {F}}$$ -transforms). By employing this method, we obtain an analytical approximate solution to the main problem in terms of flexible basic functions. The non-local 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 are demonstrated in detail. We give some examples to illustrate the significant features of the method.