Certain implementations in fractional calculus operators involving Mittag-Leffler-confluent hypergeometric functions

Abstract

The Mittag-Leffler function and confluent hypergeometric functions were created to approximate interpolation in exponential functions. The researchers noted that Prabhakar’s integral transformation, which involves extended multi-parameter Mittag-Leffler functions, may be used to create and explore different fractional calculus models. This four-parameter function is further illustrated in graphs using MATLAB. With classical (Riemann–Liouville) fractional integrals, the research shows a set of formulations for these fractional differintegral operators. Moreover, using AB Model results of Prabhakar and the generalized Prabhakar models, the authors use a series of formulae to come up with new results. This paper demonstrates how this series formula may be used to provide simple alternative evidence for numerous well-known effects of Prabhakar differintegrals.