Discrete Fractional Calculus, Local Fractional Inequalities, and Applications

Dear Colleagues,

Despite the existence of a great investigation of the continuous fractional calculus, there was not much development of the discrete fractional calculus until the last decade.  Recent research has proved that the powerful discrete fractional calculus possesses several unexpected technical complications and a huge possibility to describe real-world problems from all fields of science and engineering.

An interesting subject in connection to classical inequalities is their extension to fractal spaces via the local fractional calculus. The primary task of the local fractional calculus is to handle various non-differentiable problems appearing in complex systems of real-world phenomena. In particular, the non-differentiability occurring in science and engineering has been modeled by the local fractional ordinary or partial differential equations. Although arising from real-world phenomena, the local fractional calculus is also an important tool in pure mathematics.

Recently, a whole variety of classical real inequalities has been extended to hold on to certain fractal spaces. A rich collection of generalizations includes inequalities with more general kernels, weight functions, integration domains, and extension to a multidimensional case. A particular emphasis is dedicated to a class of inequalities with a homogeneous kernel. Namely, one imposes some weak conditions for which the constants appearing on the right-hand sides of such local fractional inequalities are the best possible.

Also, refined and reversed relations are obtained in a general multidimensional case.

We invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of discrete fractional calculus, local fractional inequalities, and their multidisciplinary applications.

Prof. Dr. Predrag Vuković
Prof. Dr. Dumitru Baleanu
Dr. Devendra Kumar
Guest Editors

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