Results 41 to 50 of about 147 (119)

New generalized Pólya–Szegö and Čebyšev type inequalities with general kernel and measure

Advances in Difference Equations, 2020
It is always attractive and motivating to acquire the generalizations of known results. In this article, we introduce a new class C ( h ) $\mathfrak{C(h)}$ of functions which can be represented in a form of integral transforms involving general kernel ...
S. Iqbal, M. Samraiz, Thabet Abdeljawad, Kottakkaran Sooppy Nisar, G. Rahman, M. Adil Khan   +5 more
doaj   +1 more source

A Comprehensive Review on the Fejér-Type Inequality Pertaining to Fractional Integral Operators

Axioms, 2023
A review of the results on the fractional Fejér-type inequalities, associated with different families of convexities and different kinds of fractional integrals, is presented.
Muhammad Tariq, Sotiris K. Ntouyas, Asif Ali Shaikh   +2 more
doaj   +1 more source

Error Bound of Hermite–Hadamard–Mercer Inequalities via ψ−Conformable Fractional Integral Operators on the Coordinates

International Journal of Mathematics and Mathematical Sciences, Volume 2026, Issue 1, 2026.
This paper develops a family of Hermite–Hadamard–Mercer‐type inequalities within the framework of generalized conformable fractional calculus. By interpreting generalized conformable fractional integrals as weighted integral means depending on the order parameter, we derive refined two‐sided bounds for coordinated convex functions that incorporate ...
Jen Chieh Lo, Mohammad Rezwan Habib
wiley   +1 more source

Solution of Time‐Fractional Coupled Burgers Equations by the Yang Transform Adomian Decomposition Method

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, the Yang transform Adomian decomposition method (YTADM) is employed in the solution of nonlinear time‐fractional coupled Burgers equations. The technique solves the fractional and nonlinear terms successfully via the Adomian decomposition of the Yang transform.
Mustafa Ahmed Ali, Mehmet Merdan, Yeou Jiann Lim   +2 more
wiley   +1 more source

New General Integral Inequalities for Polynomial Convexity in the Framework of k‐Riemann–Liouville Fractional Operators

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
The Hermite–Hadamard inequality, which is widely recognized and studied in the field of inequalities, and the k‐Riemann–Liouville fractional integral inequality, which is a generalization of the Riemann–Liouville fractional operator in operator theory, play a significant role in the existing literature concerning the concept of inequality.
Çetin Yıldız, Ferhat Polat, Fady Hasan, Nabil Mlaiki, Oluwole D. Makinde   +4 more
wiley   +1 more source

The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

Demonstratio Mathematica, 2019
In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several ...
Usta Fuat, Sarıkaya Mehmet Zeki
doaj   +1 more source

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

Residual-certified super-clocks for a time-forced Kawahara equation with Caputo-Katugampola memory

Frontiers in Physics
In this investigation, a residual-certified construction is developed for analyzing a time-forced Kawahara equation with Caputo-Katugampola memory. The main point is that the external forcing is not inserted through a classical primitive.
Weaam Alhejaili, Alvaro H. Salas, Samir A. El-Tantawy, Samir A. El-Tantawy   +3 more
doaj   +1 more source

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 Hilfer generalized proportional fractional derivative

Advances in Difference Equations, 2020
Motivated by the Hilfer and the Hilfer–Katugampola fractional derivative, we introduce in this paper a new Hilfer generalized proportional fractional derivative, which unifies the Riemann–Liouville and Caputo generalized proportional fractional ...
Idris Ahmed, Poom Kumam, Fahd Jarad, Piyachat Borisut, Wachirapong Jirakitpuwapat   +4 more
doaj   +1 more source