scholarly journals On generalized fractional integral operator associated with generalized Bessel-Maitland function

2021 ◽  
Vol 7 (2) ◽  
pp. 3027-3046
Author(s):  
Rana Safdar Ali ◽  
◽  
Saba Batool ◽  
Shahid Mubeen ◽  
Asad Ali ◽  
...  
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Transform ◽  
Fractional Integral Operator ◽  
Fractional Operator ◽  
Fractional Operators ◽  
Generalized Fractional Integral ◽  
Relationship Of ◽  
The Relationship

<abstract><p>In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.</p></abstract>

scholarly journals NEW GENERALIZATIONS IN THE SENSE OF THE WEIGHTED NON-SINGULAR FRACTIONAL INTEGRAL OPERATOR

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040003 ◽  
Author(s):  
SAIMA RASHID ◽  
ZAKIA HAMMOUCH ◽  
DUMITRU BALEANU ◽  
YU-MING CHU
Keyword(s):  
Integral Operator ◽  
Weight Function ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operator ◽  
Fractional Operators ◽  
Reverse Hölder Inequalities ◽  
Reverse Hölder

In this paper, we propose a new fractional operator which is based on the weight function for Atangana–Baleanu [Formula: see text]-fractional operators. A motivating characteristic is the generalization of classical variants within the weighted [Formula: see text]-fractional integral. We aim to establish Minkowski and reverse Hölder inequalities by employing weighted [Formula: see text]-fractional integral. The consequences demonstrate that the obtained technique is well-organized and appropriate.

scholarly journals Denoising Algorithm Based on Generalized Fractional Integral Operator with Two Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Hamid A. Jalab ◽  
Rabha W. Ibrahim
Keyword(s):  
Visual Perception ◽  
Integral Operator ◽  
Image Denoising ◽  
Digital Image ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Smoothing Filter ◽  
Generalized Fractional Integral ◽  
Two Parameters

In this paper, a novel digital image denoising algorithm called generalized fractional integral filter is introduced based on the generalized Srivastava-Owa fractional integral operator. The structures ofn×nfractional masks of this algorithm are constructed. The denoising performance is measured by employing experiments according to visual perception and PSNR values. The results demonstrate that apart from enhancing the quality of filtered image, the proposed algorithm also reserves the textures and edges present in the image. Experiments also prove that the improvements achieved are competent with the Gaussian smoothing filter.

scholarly journals Certain new weighted estimates proposing generalized proportional fractional operator in another sense

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Thabet Abdeljawad ◽  
Saima Rashid ◽  
A. A. El-Deeb ◽  
Zakia Hammouch ◽  
Yu-Ming Chu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Mathematical Physics ◽  
Fractional Integral Operator ◽  
Fractional Operator ◽  
Weighted Estimates ◽  
Fractional Differential ◽  
Positive Functions ◽  
Katugampola Fractional Integral ◽  
Hadamard Fractional Integral

Abstract The present work investigates the applicability and effectiveness of generalized proportional fractional integral ($\mathcal{GPFI}$ GPFI ) operator in another sense. We aim to derive novel weighted generalizations involving a family of positive functions n ($n\in \mathbb{N}$ n ∈ N ) for this recently proposed operator. As applications of this operator, we can generate notable outcomes for Riemann–Liouville ($\mathcal{RL}$ RL ) fractional, generalized $\mathcal{RL}$ RL -fractional operator, conformable fractional operator, Katugampola fractional integral operator, and Hadamard fractional integral operator by changing the domain. The proposed strategy is vivid, explicit, and it can be used to derive new solutions for various fractional differential equations applied in mathematical physics. Certain remarkable consequences of the main theorems are also figured.

scholarly journals Sharp Weighted Bounds for Fractional Integral Operators in a Space of Homogeneous Type

2014 ◽  
Vol 114 (2) ◽  
pp. 226 ◽  
Author(s):  
Anna Kairema
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Operator Norm ◽  
Fractional Integral Operator ◽  
Weighted Spaces ◽  
Space Of Homogeneous Type ◽  
Homogeneous Type ◽  
Fractional Integral Operators ◽  
The Relationship

We consider a version of M. Riesz fractional integral operator on a space of homogeneous type and show an analogue of the well-known Hardy-Littlewood-Sobolev theorem in this context. In our main result, we investigate the dependence of the operator norm on weighted spaces on the weight constant, and find the relationship between these two quantities. It it shown that the estimate obtained is sharp in any given space of homogeneous type with infinitely many points. Our result generalizes the recent Euclidean result by Lacey, Moen, Pérez and Torres [21].

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