The Generalized (k, ϑ)-Fractional Integral and Derivative Operators: Advances in Fractional Calculus

Abstract

In this paper, we introduce the modified conformable fractional derivative and fractional integral operators, the so called (k, ϑ)-conformable fractional derivative (CFD) and (k, ϑ)-conformable fractional integral (CFI) operators. We examine their properties, including semi-group properties and the composition of CFD and CFI operators. Furthermore, we investigate the (k, ϑ)- Conformable Caputo Fractional Derivatives. Some properties are discussed graphically. The operators defined in this paper are the generalization of distinct operators cited therein literature. These generalized operators can easily be reduced to classical operators by giving certain specific values to the parameters.