Hermite–Hadamard type inequalities for multiplicative Riemann–Liouville fractional integrals

T Du, Y Peng - Journal of Computational and Applied Mathematics, 2024 - Elsevier
In this paper, we present a multiplicative fractional integral identity. Based upon it, we
establish the Hermite–Hadamard type inequalities for multiplicatively convex functions via …

On the fractional double integral inclusion relations having exponential kernels via interval-valued co-ordinated convex map**s

T Du, T Zhou - Chaos, Solitons & Fractals, 2022 - Elsevier
In the present study, over a rectangle from the plane R 2, we define and develop the
conceptions of the interval-valued fractional double integrals having exponential kernels …

[HTML][HTML] Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities

MB Khan, G Santos-García, MA Noor… - Chaos, Solitons & …, 2022 - Elsevier
The theory of convex map** has a lot of applications in the field of applied mathematics
and engineering. The fuzzy Riemann-Liouville fractional integrals are the most significant …

On the Bullen-type inequalities via generalized fractional integrals and their applications

T Du, C Luo, Z Cao - Fractals, 2021 - World Scientific
By using generalized fractional integrals, some Bullen-type inequalities are derived where
the first derivative of considered functions is Lipschitzian, bounded or generalized (s, m) …

[HTML][HTML] On fuzzy fractional integral operators having exponential kernels and related certain inequalities for exponential trigonometric convex fuzzy-number valued …

MB Khan, HA Othman, G Santos-García, T Saeed… - Chaos, Solitons & …, 2023 - Elsevier
The most important operator in fractional theory that enables the classical theory of integrals
to be generalized is the Riemann-Liouville fractional integrals. In this paper, we have …

On the fractional integral inclusions having exponential kernels for interval-valued convex functions

T Zhou, Z Yuan, T Du - Mathematical Sciences, 2023 - Springer
The purpose of the present paper is to establish certain fractional integral inclusions having
exponential kernels, which are related to the Hermite–Hadamard, Hermite–Hadamard …

Estimations of bounds on the multiplicative fractional integral inequalities having exponential kernels

Y Peng, H Fu, T Du - Communications in Mathematics and Statistics, 2024 - Springer
To investigate the fractional Hermite–Hadamard-type inequalities, a class of the
multiplicative fractional integrals having exponential kernels is introduced. Some estimations …

Certain error bounds on the parameterized integral inequalities in the sense of fractal sets

Y Yu, J Liu, T Du - Chaos, Solitons & Fractals, 2022 - Elsevier
The objective of this study is to research certain integral inequalities with a parameter
through the generalized (s, P)-preinvex map**s in the frame of fractal space. In view of …

Hermite-Hadamard inequalities in fractional calculus for left and right harmonically convex functions via interval-valued settings

MB Khan, JE Macías-Díaz, S Treanțǎ… - Fractal and …, 2022 - mdpi.com
The purpose of this study is to define a new class of harmonically convex functions, which is
known as left and right harmonically convex interval-valued function (LR-𝓗-convex IV-F) …

Some new Hermite–Hadamard type inequalities pertaining to generalized multiplicative fractional integrals

A Kashuri, SK Sahoo, M Aljuaid, M Tariq, M De La Sen - Symmetry, 2023 - mdpi.com
There is significant interaction between the class of symmetric functions and other types of
functions. The multiplicative convex function class, which is intimately related to the idea of …