Solving variable-order fractional delay differential algebraic equations via fuzzy systems with application in delay optimal control problems

In this paper, a new approach based on fuzzy systems is used for solving variable-order fractional delay differentialalgebraic equations. The fractional derivatives are considered in the Atangana-Baleanu sense that is a new derivativewith the non-singular and non-local kernel. By relying on the ability of fuzzy systems in function approximation,the fuzzy solutions of variables are substituted in variable-order fractional delay differential algebraic equations. Theobtained algebraic equations system is then transformed into an error function minimization problem. A learningalgorithm is used to achieve the adjustable parameters of fuzzy solutions. It is shown that the variable-order fractionaldelay optimal control problems can be reformulated as variable-order fractional delay differential algebraic equationsand solved by the proposed method. The efficiency and accuracy of the presented approach are assessed through someillustrative examples of the variable-order fractional delay differential algebraic equations