Results 1 to 10 of about 145 (127)

Results on Katugampola Fractional Derivatives and Integrals

International Journal of Analysis and Applications, 2023
In this paper, we introduce and develop a new definitions for Katugampola derivative and Katugampola integral. In particular, we defined a (left) fractional derivative starting from a of a function f of order α∈(m-1, m] and a (right) fractional ...
Iqbal H. Jebril, Mohammed S. El-Khatib, Ahmad A. Abubaker, Suha B. Al-Shaikh, Iqbal M. Batiha   +4 more
doaj   +2 more sources

On the generalization of Hermite-Hadamard type inequalities for E`-convex function via fractional integrals [PDF]

Heliyon
The main motivation in this article is to prove new integral identities and related results. In this paper, we deal with E`-convex function, Hermite-Hadamard type inequalities, and Katugampola fractional integrals.
Muhammad Sadaqat Talha, Tasawar Abbas, Zhixiong Li, Amor Rebey, Affaq Ahmed, Sanaa Anjum   +5 more
doaj   +2 more sources

HERMITE–HADAMARD TYPE INEQUALITIES FOR KATUGAMPOLA FRACTIONAL INTEGRALS

Journal of Applied Analysis and Computation, 2023
Summary: In the paper, basing on the Katugampola fractional integrals \({}^\rho\mathcal{K}^\alpha_{a+}f\) and \({}^\rho\mathcal{K}^\alpha_{b-}f\) with \(f\in\mathfrak{X}_c^p(a, b) \), the authors establish the Hermite-Hadamard type inequalities for convex functions, give their left estimates, and apply these newly-established inequalities to special ...
Wang, Shu-Hong, Hai, Xu-Ran
exaly   +2 more sources

Better Approximation of Integral Form of Midpoint Formula Using p-Convex Function via Katugampola Fractional Integrals

Journal of Function Spaces
In this article, new estimations of the integral form of the midpoint formula are derived for p-convex functions via Katugampola fractional integrals.
Muhammad Latif, Saima Riaz, Khuram Ali Khan, Ammara Nosheen, Michael Kikomba Kahungu   +4 more
doaj   +2 more sources

Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals

Karpatsʹkì Matematičnì Publìkacìï, 2022
A new generalization of the Katugampola generalized fractional integrals in terms of the Mittag-Leffler functions is proposed. Consequently, new generalizations of the Hermite-Hadamard inequalities by this newly proposed fractional integral operator, for
M. Omaba
doaj   +2 more sources

New adaptive memory stochastic fractional operators and their applications in computational intelligence [PDF]

Scientific Reports
This paper introduces a new family of adaptive memory fractional integral and derivative operators designed for second-order stochastic processes in the mean-square (m.s.) sense.
Tahir Ullah Khan, Badriah Saleh AL-Juaid, Christine Markarian   +2 more
doaj   +2 more sources

Ostrowski type inequalities via the Katugampola fractional integrals

AIMS Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Erhan Set
exaly   +4 more sources

Extension of Milne-type inequalities to Katugampola fractional integrals

Boundary Value Problems
This study explores the extension of Milne-type inequalities to the realm of Katugampola fractional integrals, aiming to broaden the analytical tools available in fractional calculus.
Abdelghani Lakhdari, Hüseyin Budak, Muhammad Uzair Awan, Badreddine Meftah   +3 more
doaj   +4 more sources

Weddle's Inequality via Katugampola Fractional Integrals

Universal Journal of Mathematics and Applications
Integral inequalities represent an important and ongoing area of study in mathematical understanding. Due to their extensive use in science, fractional calculus approaches have been the subject of a great deal of research recently.
Jamal El-achky
doaj   +2 more sources

Better Approximation of Milne-Type Inequalities via Convex Functions and ABK Fractional Integral Operators

Journal of Applied Mathematics
In this paper, we give an identity for the function which is twice differentiable. Through the applications of this identity and Atangana–Baleanu–Katugampola (ABK) fractional integrals, several fractional Milne-type inequalities are derived for functions
Muhammad Bilal Ahmed, Khuram Ali Khan, Ammara Nosheen, Ndolane Sene   +3 more
doaj   +2 more sources