Advances in Fractional Integral Inequalities: Theory and Applications

Dear Colleagues,

The flexibility of fractional calculus has empowered researchers to develop a wide range of convex integral inequalities that are fundamental in approximation theory. Classical inequalities, such as Jensen’s, Simpson’s, Ostrowski’s, Hermite–Hadamard’s, and trapezoidal inequalities, are commonly used to establish error bounds in numerical integration. To derive these inequalities, researchers employ various approaches, including the use of fractional operators, functional maps, relational frameworks, and other advanced analytical techniques, underscoring the significant influence of fractional calculus in contemporary mathematical analysis. For example, self-adjoint operators, which are fundamental in both mathematics and physics, facilitate the extension of classical numerical inequalities to linear operators on Hilbert spaces. These operators, which generalize Hermitian matrices, are defined by their symmetry, guaranteeing real eigenvalues and orthogonal eigenvectors. The analysis of inequalities involving self-adjoint operators has profound applications in functional analysis, quantum mechanics, operator theory, and optimization.

The main objective of this Special Issue is to continue research on the development of fundamental aspects of fractional integral inequalities, as well as their potential applications. Topics that are invited for submission include (but are not limited to) the following:

• Theory of fractional integral inequalities;
• Numerical integration methods;
• Applications of fractional integral inequalities on operator theory;
• Applications of fractional integral inequalities on quantum mechanics.

Dr. Luis A. Gallegos-Infante
Prof. Dr. Jorge E. Macías Díaz
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fractal and Fractional is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.