scholarly journals Fractional Operators Associated with the ք -Extended Mathieu Series by Using Laplace Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Hafte Amsalu Kahsay ◽  
Adnan Khan ◽  
Sajjad Khan ◽  
Kahsay Godifey Wubneh
Keyword(s):  
Integral Operator ◽  
Laplace Transform ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
The Laplace Transform ◽  
Mathieu Series

In this paper, our leading objective is to relate the fractional integral operator known as P δ -transform with the ք -extended Mathieu series. We show that the P δ -transform turns to the classical Laplace transform; then, we get the integral relating the Laplace transform stated in corollaries. As corollaries and consequences, many interesting outcomes are exposed to follow from our main results. Also, in this paper, we have converted the P δ -transform into a classical Laplace transform by changing the variable ln δ − 1 s + 1 / δ − 1 ⟶ s ; then, we get the integral involving the Laplace transform.

scholarly journals ON THEOREMS CONNECTING THE LAPLACE TRANSFORM AND A GENERALIZED FRACTIONAL INTEGRAL OPERATOR

1998 ◽  
Vol 29 (4) ◽  
pp. 323-333
Author(s):  
K. C. GUPTA ◽  
S. P. GOYAL ◽  
TARIQ O. SALIM
Keyword(s):  
Integral Operator ◽  
Laplace Transform ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Integral Operators ◽  
The Laplace Transform ◽  
Generalized Fractional Integral ◽  
Generalized Fractional Integral Operators

The aim of the present paper is to establish two theorems connecting the Laplace transform and a certain class of generalized fractional integral operators involving a generalized polynom叫 set. These theorems provide .usful extension and unification of a number of (known or new) results for vaious classes of fractional integral operators. Several interesting applications of the main theorems are also mentioned briefly.

scholarly journals Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ahmet Ocak Akdemir ◽  
Ali Karaoğlan ◽  
Maria Alessandra Ragusa ◽  
Erhan Set
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Concave Functions ◽  
Fractional Operators ◽  
Fractional Integral Operators

Recently, many fractional integral operators were introduced by different mathematicians. One of these fractional operators, Atangana-Baleanu fractional integral operator, was defined by Atangana and Baleanu (Atangana and Baleanu, 2016). In this study, firstly, a new identity by using Atangana-Baleanu fractional integral operators is proved. Then, new fractional integral inequalities have been obtained for convex and concave functions with the help of this identity and some certain integral inequalities.

scholarly journals A Note on Reverse Minkowski Inequality via Generalized Proportional Fractional Integral Operator with respect to Another Function

2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Saima Rashid ◽  
Fahd Jarad ◽  
Yu-Ming Chu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Nonlinear Behavior ◽  
Minkowski Inequality ◽  
Coupled Systems ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Exponential Functions ◽  
Physical Systems ◽  
Small Parameters

This study reveals new fractional behavior of Minkowski inequality and several other related generalizations in the frame of the newly proposed fractional operators. For this, an efficient technique called generalized proportional fractional integral operator with respect to another function Φ is introduced. This strategy usually arises as a description of the exponential functions in their kernels in terms of another function Φ. The prime purpose of this study is to provide a new fractional technique, which need not use small parameters for finding the approximate solution of fractional coupled systems and eliminate linearization and unrealistic factors. Numerical results represent that the proposed technique is efficient, reliable, and easy to use for a large variety of physical systems. This study shows that a more general proportional fractional operator is very accurate and effective for analysis of the nonlinear behavior of boundary value problems. This study also states that our findings are more convenient and efficient than other available results.

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 MORREY SPACES AND FRACTIONAL OPERATORS

2010 ◽  
Vol 88 (2) ◽  
pp. 247-259 ◽  
Author(s):  
HITOSHI TANAKA
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Fractional Integral ◽  
Morrey Spaces ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Fractional Maximal Operator

AbstractThe relation between the fractional integral operator and the fractional maximal operator is investigated in the framework of Morrey spaces. Applications to the Fefferman–Phong and the Olsen inequalities are also included.

scholarly journals On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 223
Author(s):  
Erhan Set ◽  
Ahmet Ocak Akdemir ◽  
Ali Karaoǧlan ◽  
Thabet Abdeljawad ◽  
Wasfi Shatanawi
Keyword(s):  
Applied Sciences ◽  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Hadamard Inequality ◽  
Fractional Integral Operators ◽  
Inequality Theory ◽  
Fractional Analysis

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.

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 Fractional Operators in p -adic Variable Exponent Lebesgue Spaces and Application to p -adic Derivative

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Leonardo Fabio Chacón-Cortés ◽  
Humberto Rafeiro
Keyword(s):  
Cauchy Problem ◽  
Integral Operator ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Fractional Operators ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Spaces ◽  
Uniqueness Of The Solution

In this paper, we prove the boundedness of the fractional maximal and the fractional integral operator in the p -adic variable exponent Lebesgue spaces. As an application, we show the existence and uniqueness of the solution for a nonhomogeneous Cauchy problem in the p -adic variable exponent Lebesgue spaces.

A note on fractional integral operator associated with multiindex Mittag-Leffler functions

Filomat ◽  
2016 ◽  
Vol 30 (7) ◽  
pp. 1931-1939 ◽  
Author(s):  
Junesang Choi ◽  
Praveen Agarwal
Keyword(s):  
Integral Operator ◽  
Fractional Calculus ◽  
Fractional Integral ◽  
Fractional Integration ◽  
Fractional Integral Operator ◽  
Integration Formula ◽  
Special Cases

Recently Kiryakova and several other ones have investigated so-called multiindex Mittag-Leffler functions associated with fractional calculus. Here, in this paper, we aim at establishing a new fractional integration formula (of pathway type) involving the generalized multiindex Mittag-Leffler function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

Sign in / Sign up

Export Citation Format

Share Document