A validation on concept of formula for variable order integral and derivatives

Abstract

This paper deals and addresses the query that which of the variable order operators are reasonable and regular extension of constant order operators. An irregularity is pointed out in the definition of variable order operators. We generalize some existing results of constant order to variable order using special functions of fractional calculus. It provides a method for considering the existence of solution for variable order fractional differential equations. Some illustrations are presented to support the validity of variable order operators. Further, we consider an application of a class of fractional initial value problems and provide the criteria of existence and uniqueness of its solution with example.