Fractional Calculus Operators and the Mittag-Leffler Function, 2nd Edition

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 science, especially in numerical analysis and various fields of physics and engineering. Fractional calculus enabled the adoption of a theoretical model based on experimental data.

Inequalities that 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 the 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.

As a solution of fractional order differential or integral equations, the Mittag-Leffler function with its generalizations appears. Extensions and generalizations of the Mittag-Leffler function enabled researchers to obtain fractional integral inequalities of different types. Consequently, new results are produced for a more generalized fractional integral operator containing the Mittag-Leffler function in their kernels.

Dr. Maja Andrić
Guest Editor

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• fractional calculus
• mittag-Leffler function
• fractional integral operator
• integral inequality
• convex function
• bound of operator