Results 41 to 50 of about 463 (144)

Some fractional integral inequalities for the Katugampola integral operator

AIMS Mathematics, 2019
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Ravi Shanker Dubey, Pranay Goswami
openaire   +2 more sources

New Generalized the Hermite-Hadamard Inequality and Related Integral Inequalities Involving Katugampola Type Fractional Integrals [PDF]

Symmetry, 2020
In this paper, a new identity for the generalized fractional integral is defined, through which new integral inequality for functions whose first derivatives in absolute value are convex. The new generalized Hermite-Hadamard inequality for generalized convex function on fractal sets involving Katugampola type fractional integral is established.
Ohud Almutairi, Adem Kılıçman
openaire   +1 more source

Ostrowski-type inequalities for n-polynomial P $\mathscr{P}$ -convex function for k-fractional Hilfer–Katugampola derivative

Journal of Inequalities and Applications, 2021
In this article, we develop a novel framework to study a new class of convex functions known as n-polynomial P $\mathscr{P} $ -convex functions. The purpose of this article is to establish a new generalization of Ostrowski-type integral inequalities by ...
Samaira Naz, Muhammad Nawaz Naeem, Yu-Ming Chu   +2 more
doaj   +1 more source

New fractional integral inequalities pertaining 2D–approximately coordinate (r1,ℏ1)-(r2,ℏ2)–convex functions

Alexandria Engineering Journal, 2022
In this article the authors introduce the concept of two dimensional approximately coordinate (r1,ℏ1)–(r2,ℏ2)–convex function that generalize several known coordinate convexity classes.
Ying-Qing Song, Saad Ihsan Butt, Artion Kashuri, Jamshed Nasir, Muhammad Nadeem   +4 more
doaj   +1 more source

The mean value theorem and Taylor's theorem for fractional derivatives with Mittag-Leffler kernel. [PDF]

, 2018
We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag-Leffler kernel.
Baleanu, Dumitru, Fernandez, Arran
core   +2 more sources

New conticrete inequalities of the Hermite-Hadamard-Jensen-Mercer type in terms of generalized conformable fractional operators via majorization

Demonstratio Mathematica, 2023
The Hermite-Hadamard inequality is regarded as one of the most favorable inequalities from the research point of view. Currently, mathematicians are working on extending, improving, and generalizing this inequality.
Saeed Tareq, Khan Muhammad Adil, Faisal Shah, Alsulami Hamed H., Alhodaly Mohammed Sh.   +4 more
doaj   +1 more source

A Comprehensive Review of the Hermite–Hadamard Inequality Pertaining to Fractional Integral Operators

Mathematics, 2023
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 Hermite–Hadamard (H-H)-type inequalities ...
Muhammad Tariq, Sotiris K. Ntouyas, Asif Ali Shaikh   +2 more
doaj   +1 more source

Mellin Transforms of the Generalized Fractional Integrals and Derivatives

, 2014
We obtain the Mellin transforms of the generalized fractional integrals and derivatives that generalize the Riemann-Liouville and the Hadamard fractional integrals and derivatives.
Bucchianico, Butkovskii, Butzer, Butzer, Butzer, Butzer, Bóna, Erdélyi, Erdélyi, Flajolet, Gaboury, Goldman, Hadamard, Herrmann, Katugampola, Katugampola, Kilbas, Kilbas, Kilbas, Kilbas, Kiryakova, Machado, Miller, Noor, Noor, Noor, Odzijewicz, Odzijewicz, Odzijewicz, Oldham, Podlubny, Pooseh, Robbins, Robinson, Rodrigues, Roman, Roman, Roman, Rota, Rota, Samko, Udita N. Katugampola, Yakubovich   +42 more
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Fractional calculus of variations in terms of a generalized fractional integral with applications to physics [PDF]

, 2012
We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives.
Malinowska, A.B., Odzijewicz, T., Torres, D.F.M.   +2 more
core   +11 more sources

New Integral Inequalities via the Katugampola Fractional Integrals for Functions Whose Second Derivatives Are Strongly η-Convex

Mathematics, 2019
In this paper, we introduced some new integral inequalities of the Hermite⁻Hadamard type for functions whose second derivatives in absolute values at certain powers are strongly η -convex functions via the Katugampola fractional integrals.
Seth Kermausuor, Eze R. Nwaeze, Ana M. Tameru   +2 more
doaj   +1 more source