Type of Leibniz Rule on Riemann-Liouville Variable-Order Fractional Integral and Derivative Operator

Abstract

In this paper, types of Leibniz Rule for Riemann-Liouville Variable-Order fractional integral and derivative Operator is developed. The product rule, quotient rule, and chain rule formulas for both integral and differential operators are established. In particular, there are four types of product rule formulas: Product rule type-I, Product rule type-II, Product rule type-III, and Product rule type-Iv. Quotient rule type-I, quotient rule type-II, quotient rule type-III, and quotient rule type-Iv formulas developed from product rule types. There are four types of chain rule formulas: chain rule type-I, chain rule type-II, chain rule type-III, and chain rule type-Iv.