A Review of Generalized Fractional Integral Operator in Fractional Differential Equations

Exploring the Applications and Properties of Generalized Fractional Integral Operators in Fractional Differential Equations

Abstract

As a result of its wide range of applications in science during the past several years,academics have focused a great deal of attention on fractional calculus (FC). Multivariate Mittag–Lefflerfunctions are considered strong extensions of the traditional Mittag–Leffler functions in fractionalcalculus. An integral operator with a multivariate Mittag–Leffler (M-L) function is introduced in this study.For example, we show that an infinite series of Riemann–Liouville integrals can be expanded, theLaplace transform (LT), semigroup property can be shown, and composition with Riemann–Liouvilleintegrals can be proved for the proposed operators. Also, we discuss the features of fractionaldifferential operators. The suggested operators like the fractional kinetic differential and the timefractionalheat equation are also explored.