Results 31 to 40 of about 1,529 (136)

A comprehensive review of the Pachpatte-type inequality pertaining to fractional integral operators [PDF]

Surveys in Mathematics and its Applications
In the frame of fractional calculus, the term convexity is primarily utilized to address several challenges in both pure and applied research. The main focus and objective of this review paper is to present Pachpatte-type inequalities involving a variety
Muhammad Tariq, Asif Ali Shaikh, Sotiris K. Ntouyas   +2 more
doaj  

Fractional Moment Theory for Anomalous Transport: A Unified Framework for Lévy Flights, Fractals, and Complex Dynamical Systems

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 14964-15009, 15 September 2026.
ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley   +1 more source

On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces

Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 15358-15384, 15 September 2026.
ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
wiley   +1 more source

Fractional Integral Inequalities of Riemann–Liouville Type for Higher‐Order Differentiable Convex Mappings

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12313-12323, 30 July 2026.
ABSTRACT In this paper, we investigate several Riemann–Liouville fractional integral inequalities for higher‐order differentiable functions using a simple and novel approach. First, we present an inequality involving fractional integrals that generalizes the right‐hand side of the fundamental Hermite–Hadamard inequality to higher‐order derivatives ...
Samet Erden, Hüseyin Budak
wiley   +1 more source

On Fractional Hermite–Hadamard-Type Inequalities for Harmonically s-Convex Stochastic Processes

Fractal and Fractional
In this paper, we investigate Hermite–Hadamard-type inequalities for harmonically s-convex stochastic processes via Riemann–Liouville fractional integrals. We begin by introducing the notion of harmonically s-convex stochastic processes. Subsequently, we
Rabab Alzahrani, Raouf Fakhfakh, Ghadah Alomani, Badreddine Meftah   +3 more
doaj   +1 more source

Some New Generalizations for Exponentially s-Convex Functions and Inequalities via Fractional Operators

Fractal and Fractional, 2019
The main objective of this paper is to obtain the Hermite−Hadamard-type inequalities for exponentially s-convex functions via the Katugampola fractional integral.
Saima Rashid, Muhammad Aslam Noor, Khalida Inayat Noor, Ahmet Ocak Akdemir   +3 more
doaj   +1 more source

Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,qx$$ {M}_n^{\left(p,q\right)}(x) $$

Mathematical Methods in the Applied Sciences, Volume 49, Issue 11, Page 12524-12538, 30 July 2026.
ABSTRACT Constructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szegő‐Hermite polynomials, in the literature.
Esra Güldoğan Lekesiz
wiley   +1 more source

Wirtinger-type inequalities for Caputo fractional derivatives via Taylor’s formula

Journal of Inequalities and Applications
In this study, we firstly derive a Wirtinger-type result, which gives the connection in between the integral of square of a function and the integral of square of its Caputo fractional derivatives with the help of left-sided and right-sided fractional ...
Samet Erden, Mehmet Zeki Sarıkaya, Burçin Gokkurt Ozdemir, Neslihan Uyanık   +3 more
doaj   +1 more source

Some generalized Riemann-Liouville k-fractional integral inequalities

Journal of Inequalities and Applications, 2016
The focus of the present study is to prove some new Pólya-Szegö type integral inequalities involving the generalized Riemann-Liouville k-fractional integral operator.
Praveen Agarwal, Jessada Tariboon, Sotiris K Ntouyas   +2 more
doaj   +1 more source

New Approach to Weighted Newton‐Type Inequalities Using Riemann–Liouville Fractional Integrals

Mathematical Methods in the Applied Sciences, Volume 49, Issue 10, Page 11186-11204, 15 July 2026.
ABSTRACT In this investigation paper, we present some weighted inequalities Newton‐type for various classes of functions utilizing Riemann–Liouville fractional integrals. The study begins by introducing a positive weighted function to derive a key integral equality essential for proving the main results.
Rubayyi T. Alqahtani, Hüseyin Budak
wiley   +1 more source