University of Split, Croatia
Fractional integral inequalities for convex functions
Thursday, 30 November 2023 at 17:10
On line: https://meet.google.com/nif-zfwd-mrg
Abstract
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. Our recently introduced new class of (h,g.m)-convex functions unifies a certain range of convexity, thus allowing the generalizations of know results. The goal is to apply inequalities of classical types to this class and to give them in more general settings using fractional calculus, for the purpose of their extension, generalization and improvement of boundary evaluations.
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