Local Fractional Integral Hölder-Type Inequalities and Some Related Results

Abstract

This paper is devoted to establishing some functional generalizations of Hölder and reverse Hölder’s inequalities with local fractional integral introduced by Yang. Then, based on the obtained results, we derive some related inequalities including local fractional integral Minkowski-type and Dresher-type inequalities, which are some extensions of several existing local fractional integral inequalities.

Certain New Reverse Hölder- and Minkowski-Type Inequalities for Modified Unified Generalized Fractional Integral Operators with Extended Unified Mittag–Leffler Functions

“…By employing the fractional quantum integrals, Yang [9] gave some fractional quantum Hölder-and Minkowski-type integral inequalities. Based on the local FIOs, Chen et al [10] investigated the Hölder-type functional inequalities and the reverse version. Furthermore, Minkowski-and Dresher-type inequalities for local FIOs were also presented.…”

A novel perspective to the local fractional Zakharov–Kuznetsov‐modified equal width dynamical model on Cantor sets

“…The traveling wave solution of ZKMEWD equation has been studied by a lot of efficient methods: homotopy method (HM), [10][11][12][13] variational iteration technology (VIT), 14,15 sine-cosine method (SCM), 16 sub-equation method (SEM), 17 scale transform method (STM), 18,19 Darboux transform method (DTM), 20 and so on. [21][22][23][24][25][26][27] In this work, we study the traveling wave solution of the nondifferentiable type for LFZKMEWD equation by a novel scheme, which is fractal variational wave method (FVWM). The proposed FVWM is efficient and easy to perform.The FVWM needs only two steps: The first step, the fractal variational principle (FVP) of LFZKMEWD equation is obtained according to using the fractal semi-inverse method (FSIM).…”

“…Equation () is a classical wave equation and is used to describe the shallow water wave. The traveling wave solution of ZKMEWD equation has been studied by a lot of efficient methods: homotopy method (HM), 10–13 variational iteration technology (VIT), 14,15 sine‐cosine method (SCM), 16 sub‐equation method (SEM), 17 scale transform method (STM), 18,19 Darboux transform method (DTM), 20 and so on 21–27 …”