Exploring fractional calculus operators in context with extended hypergeometric and confluent hypergeometric function: image formulas and applications

Abstract

Fractional calculus in mathematics has various applications in engineering and science, inequality theory and is also used in solving various integral equations. In the past few years, fractional calculus operators that contains different special functions have been discussed by many researchers. In our paper, our objective is to discuss image formulas for different fractional integral and differential operators using the extended hypergeometric and extended confluent hypergeometric function involving Appell series and Lauricella function. Fractional calculus operators that has Appell function in the kernel and Saigo fractional operator are used in this paper. The results investigated in this manuscript are general, novel and are used to discuss various special cases and more fascinating results involving other special functions and fractional calculus operators. We have also discussed the application and future scope along with a brief comparison with the existing literature.