Fractional Calculus Operators and the Mittag-Leffler Function

Among the numerous applications of the theory of fractional calculus in almost all applied sciences, applications in numerical analysis and various fields of physics and engineering stand out. Applications of inequalities involving function integrals and their derivatives, as well as applications of fractional differentiation inequalities, have motivated many researchers to investigate extensions and generalizations using various fractional differential and integral operators. Of particular importance is the Mittag–Leffler function which, with its generalizations, appears as a solution to differential or integral equations of fractional order. This produced new results for more generalized fractional integral operators containing the Mittag–Leffler function in their kernels.