Fractional Calculus Operators and the Mittag-Leffler Function

Dear Colleagues,

In recent years, considerable interest in the theory of fractional calculus has been stimulated due to its many applications in almost all applied sciences, especially in numerical analysis and various fields of physics and engineering. Fractional calculus has enabled the adoption of a theoretical model based on experimental data.

Inequalities which involve integrals of functions and their derivatives, whose study has a history of about a century, are of great importance in mathematics, with far-reaching applications in the theory of differential equations, approximations, and probability, among others.

Fractional differentiation inequalities have applications to fractional differential equations; the most important ones are in establishing uniqueness of the solution of initial problems and giving upper bounds to their solutions. These applications have motivated many researchers in the field of integral inequalities to investigate certain extensions and generalizations using different fractional differential and integral operators.

The Mittag–Leffler function with its generalizations emerges as a solution of fractional order differential or integral equations. Extensions and generalizations of the Mittag–Leffler function have enabled researchers to obtain fractional integral inequalities of different types. Consequently, new results are produced for more generalized fractional integral operators containing the Mittag–Leffler function in their kernels.

Dr. Maja Andrić
Guest Editor

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