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.

scholarly journals Estimates of Fractional Integral Operators on Variable Exponent Lebesgue Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Canqin Tang ◽  
Qing Wu ◽  
Jingshi Xu
Keyword(s):  
Integral Operator ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Weak Type ◽  
Type Inequality ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Fractional Integral Operators ◽  
Variable Exponent Lebesgue Spaces

By some estimates for the variable fractional maximal operator, the authors prove that the fractional integral operator is bounded and satisfies the weak-type inequality on variable exponent Lebesgue spaces.

scholarly journals Riemann-Liouville and Higher Dimensional Hardy Operators for NonNegative Decreasing Function inLp(·)Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Muhammad Sarwar ◽  
Ghulam Murtaza ◽  
Irshaad Ahmed
Keyword(s):  
Integral Operator ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Sufficient Conditions ◽  
Fractional Integral Operator ◽  
Lebesgue Spaces ◽  
Higher Dimensional ◽  
Necessary And Sufficient ◽  
Decreasing Functions ◽  
Hardy Operators

One-weight inequalities with general weights for Riemann-Liouville transform andn-dimensional fractional integral operator in variable exponent Lebesgue spaces defined onRnare investigated. In particular, we derive necessary and sufficient conditions governing one-weight inequalities for these operators on the cone of nonnegative decreasing functions inLp(x)spaces.

The Chen-Marchaud fractional integro-differentiation in the variable exponent Lebesgue spaces

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
Humberto Rafeiro ◽  
Makhmadiyor Yakhshiboev
Keyword(s):  
Integral Operator ◽  
Fractional Derivative ◽  
Variable Exponent ◽  
Fractional Integral ◽  
Inverse Operator ◽  
Fractional Integral Operator ◽  
Left Inverse ◽  
Fractional Differentiation ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces

AbstractAfter recalling some definitions regarding the Chen fractional integro-differentiation and discussing the pro et contra of various ways of truncation related to Chen fractional differentiation, we show that, within the framework of weighted Lebesgue spaces with variable exponent, the Chen-Marchaud fractional derivative is the left inverse operator for the Chen fractional integral operator.

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

scholarly journals The boundedness of multilinear commutators on locally compact Vilenkin groups

2006 ◽  
Vol 4 (3) ◽  
pp. 261-273 ◽  
Author(s):  
Canqin Tang
Keyword(s):  
Integral Operator ◽  
Hardy Spaces ◽  
Fractional Integral ◽  
Fractional Integral Operator ◽  
Vilenkin Group ◽  
Lebesgue Spaces ◽  
Locally Compact ◽  
Vilenkin Groups ◽  
Multilinear Commutators

LetGbe a locally compact Vilenkin group. In this paper, the authors investigate the boundedness of multilinear commutators of fractional integral operator on Lebesgue spaces onG. Furthermore, the boundedness on Hardy spaces are also obtained in this paper.

scholarly journals A New Approach for the Fractional Integral Operator in Time Scales with Variable Exponent Lebesgue Spaces

2021 ◽  
Vol 5 (1) ◽  
pp. 7
Author(s):  
Lütfi Akın
Keyword(s):  
Integral Operator ◽  
Harmonic Analysis ◽  
Time Scales ◽  
Variable Exponent ◽  
Integral Operators ◽  
Lebesgue Spaces ◽  
Important Place ◽  
New Approach ◽  
Variable Exponent Lebesgue Spaces ◽  
Important Study

Integral equations and inequalities have an important place in time scales and harmonic analysis. The norm of integral operators is one of the important study topics in harmonic analysis. Using the norms in different variable exponent spaces, the boundedness or compactness of the integral operators are examined. However, the norm of integral operators on time scales has been a matter of curiosity to us. In this study, we prove the equivalence of the norm of the restricted centered fractional maximal diamond integral operator to the norm of the centered fractional maximal diamond integral operator on time scales with variable exponent Lebesgue spaces. This study will lead to the study of problems such as the boundedness and compactness of integral operators on time scales.

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.

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