Results 61 to 70 of about 145 (127)

Visualizing Fractional Integral Inequalities Using Euler’s Beta Function and Extended Convexity

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this research article, we present various extensions and refinements of Hermite–Hadamard and related fractional integral inequalities by utilizing the unique characteristics of Euler’s beta and extended convex functions. In some of these results, Euler’s beta function is used as a weight function, while in the others, Euler’s incomplete beta ...
Muhammad Imran, Ahsan Mehmood, Shahid Mubeen, Muhammad Samraiz, Gauhar Rahman, Mohammad Sediq Safi, Aliaa Burqan   +6 more
wiley   +1 more source

Hermite-Hadamard type inequalities for harmonically convex functions via Katugampola fractional integrals [PDF]

Miskolc Mathematical Notes, 2019
In this work, firstly, we established Hermite-Hadamard's inequalities for harmonically convex functions via Katugampola fractional integrals. Then we give some Hermite-Hadamard type inequalities of these classes functions.
Mumcu, Ilker, Set, Erhan, Akdemir, Ahmet Ocak, Akdemir, Ahmet Ocak, Belirlenecek, [Mumcu, Ilker -- Set, Erhan] Ordu Univ, Dept Math, Fac Sci & Arts, Ordu, Turkey -- [Akdemir, Ahmet Ocak] Agri Ibrahim Cecen, Dept Math, Fac Sci & Arts, Agri, Turkey   +5 more
openaire   +3 more sources

Weighted Inequalities of Milne‐Type and Applications: Bridging Classical and Fractional Integrals

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this study, weighted Milne‐type inequalities are derived for classical integrals, and by selecting special weight functions, several Milne‐type inequalities are presented for well‐known fractional integrals, such as Riemann–Liouville fractional integrals, conformable fractional integrals, and tempered fractional integrals.
Hüseyin Budak, Marko Kostic
wiley   +1 more source

On Inequalities for S-Convex Function Based on Katugampola Fractional Integral

Journal of Physics: Conference Series, 2020
Abstract The subject of integral inequalities has been considered and studied by many mathematical scholars. Based on Katugampola fractional integrals in this article, authors discuss s-function and obtain some inequalities.
openaire   +1 more source

A Novel Computational Technique for Numerical Approximation of Nonlinear Fractional Dynamical Systems: Convergence and Efficiency Analysis

Journal of Function Spaces, Volume 2026, Issue 1, 2026.
In this work, we study a family of nonlinear fractional dynamical systems and propose a numerical procedure based on the power series iterative method (PSIM). The systems are formulated in terms of the Atangana–Baleanu–Caputo (ABC) fractional derivative, which is well‐suited to the modeling of memory and nonlocal effects.
Faten H. Damag, Amin Saif, Mohammed Alsharafi, Lakhlifa Sadek   +3 more
wiley   +1 more source

Exact Soliton Dynamics and Stability Analysis of a Fractional Order Coupled Wu‐Zhang System via a Generalized Riccati−Bernoulli−Bäcklund Approach

Journal of Mathematics, Volume 2026, Issue 1, 2026.
To investigate the fractional coupled Wu‐Zhang system analytically, this paper uses a hybrid generalized Riccati−Bernoulli sub‐ODE scheme and Bäcklund transformation to find the exact kink, antikink, and bright‐kink soliton solutions. The dynamical properties of these solutions are discussed using Hamiltonian formulation, phase‐portrait analysis, and ...
M. Mossa Al-Sawalha, Linda Alzaben, Asıf Yokus   +2 more
wiley   +1 more source

Inequalities for Katugampola conformable partial derivatives

Journal of Inequalities and Applications, 2019
In the paper, we introduce two concepts of Katugampola conformable partial derivatives and α-conformable integrals. As applications, we establish Opial type inequalities for Katugampola conformable partial derivatives and α-conformable integrals. The new
Chang-Jian Zhao, Wing-Sum Cheung
doaj   +1 more source

Analytical Investigation of Fractional Nonlinear Systems in Compact‐Open Banach Spaces: Applications in the Chemical Wave Propagation Theory

Journal of Mathematics, Volume 2026, Issue 1, 2026.
In this work, we present some analytical and topological framework for fractional nonlinear systems on compact‐open Banach spaces. By using the locally compact property of these spaces, the continuity and compactness of nonlinear operators are rigorously established.
Faten H. Damag, Khaled M. Saad, Mohammad Alshammari, Amin Saif, Mohammed S. Alsharafi, Smritijit Sen   +5 more
wiley   +1 more source

Some Novel Inclusions for Interval‐Valued s‐Convex Functions in the Second Sense Involving Caputo–Fabrizio Integrals

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This paper investigates the class of interval‐valued s‐convex functions in the second sense sIVC2 using Caputo–Fabrizio CF integrals. Some generalizations of the Hermite–Hadamard HH‐type, Hermite–Hadamard–Fejér HHF‐type, and Hermite–Hadamard–Mercer HHM‐type inclusions involving the CF integrals are developed.
Ammara Nosheen, Khuram Ali Khan, Mariam Aslam, Atiq ur Rehman, Demco K. Mukongo, Smritijit Sen   +5 more
wiley   +1 more source

Basic Theory for Differential Equations with Unified Reimann-Liouville and Hadamard Type Fractional Derivatives

International Journal of Analysis and Applications, 2017
In this paper, we extend the definition of the fractional integral and derivative introduced in [Appl. Math. Comput. 218 (2011)] by Katugampola, which exhibits nice properties only for numbers whose real parts lie in [0,1].
Basak Karpuz, Umut M. Ozkan, Tugba Yalcin, Mustafa K. Yildiz   +3 more
doaj   +2 more sources