Mathematical Inequalities and Fractional Calculus

Dear Colleagues,

Integral inequalities are a fundamental concept in calculus and mathematics in general. They have great importance in various fields, both theoretical and applied, such as the analysis of functions, measure theory, functional analysis, optimization and control, initial and boundary value problems, and error estimation.

In recent years, interest in the study of classical inequalities has increased. Broadly speaking, integral inequalities can be categorized into the following groups:

• Classical integral inequalities.

Inequalities that do not involve the notion of convexity: Hölder’s inequality, the power mean inequality, Minkowski’s inequality, Chebyshev’s inequality, Grüss’ inequality, and Wirtinger’s inequality.

Inequalities that use the notion of convexity: Simpson's inequality, Jensen’s (Jensen–Mercer) inequality, and the Hermite–Hadamard and Hermite–Hadamard–Fejér inequalities.

• Auxiliary integral inequalities: Hölder’s inequality, the power mean inequality, and Minkowski’s inequality.
• Integral inequalities that involve products of integrals: Chebyshev’s inequality and Grüss’ inequality.
• Integral inequalities that involve derivatives: Wirtinger’s inequality and Simpson's inequality.

Generalizations of the above inequalities are often applied to integral operators associated with different types of fractional integrals and derivatives, such as the Hadamard, Riemann–Liouville, Weil, Erdelyi–Kober, Katugampola integrals and other types defined by different mathematicians. These results have demonstrated their usefulness and potential in the modeling of different processes and phenomena.

We cordially invite interested researchers to contribute original and high-quality research on the aforementioned topics to this Special Issue.

Dr. Péter Kórus
Prof. Dr. Juan Eduardo Nápoles Valdés
Guest Editors

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• inequalities
• integral inequalities
• fractional calculus
• q-calculus
• fractional integral operator
• fractional differential operator
• fractional differential equation
• fractional integral equation