On the variable-order fractional derivatives with respect to another function

Abstract In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and the integral kernel depends on a function. We observe that in the case of variable order, the concepts are distinct, and we present relations between them. Formulas for approximating fractional derivatives are provided, involving only integer-order derivatives. Finally, we conclude the work with some simulations to exemplify the method.