$ \theta $-type generalized fractional integral and its commutator on some non-homogeneous variable exponent spaces

We study fractional variational problems in terms of a generalized fractional integral with Lagrangians depending on classical derivatives, generalized fractional integrals and derivatives. We obtain necessary optimality conditions for the basic and isoperimetric problems, as well as natural boundary conditions for free-boundary value problems. The fractional action-like variational approach (FALVA) is extended and some applications to physics discussed.

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On New Integral Inequalities Involving Generalized Fractional Integral Operators

Special Functions and Analysis of Differential Equations ◽

10.1201/9780429320026-11 ◽

2020 ◽

pp. 227-242

Author(s):

M. Emin Özdemir ◽

Ahmet Ocak Akdemir ◽

Erhan Set ◽

Alper Ekinci

Keyword(s):

Fractional Integral ◽

Integral Operators ◽

Integral Inequalities ◽

Fractional Integral Operators ◽

Generalized Fractional Integral ◽

Generalized Fractional Integral Operators

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The Boundedness of Multilinear Fractional Integral Operators with Variable Kernel on Variable Exponent Lebesgue Spaces

Pure Mathematics ◽

10.12677/pm.2016.61011 ◽

2016 ◽

Vol 06 (01) ◽

pp. 72-80

Author(s):

秋阅万

Keyword(s):

Variable Exponent ◽

Fractional Integral ◽

Integral Operators ◽

Lebesgue Spaces ◽

Variable Kernel ◽

Fractional Integral Operators ◽

Multilinear Fractional Integral ◽

Variable Exponent Lebesgue Spaces

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A Universal Predictor-corrector Algorithm for Numerical Simulation of Generalized Fractional Differential Equations

10.21203/rs.3.rs-375580/v1 ◽

2021 ◽

Author(s):

Zaid Odibat

Keyword(s):

Numerical Simulation ◽

Fractional Derivatives ◽

Fractional Integral ◽

Differential Operators ◽

Numerical Solutions ◽

Fractional Operators ◽

Initial Value ◽

Generalized Fractional Integral ◽

Fractional Differential ◽

Predictor Corrector

Abstract This study introduces some remarks on generalized fractional integral and differential operators, that generalize some familiar fractional integral and derivative operators, with respect to a given function. We briefly explain how to formulate representations of generalized fractional operators. Then, mainly, we propose a predictor-corrector algorithm for the numerical simulation of initial value problems involving generalized Caputo-type fractional derivatives with respect to another function. Numerical solutions of some generalized Caputo-type fractional derivative models have been introduced to demonstrate the applicability and efficiency of the presented algorithm. The proposed algorithm is expected to be widely used and utilized in the field of simulating fractional-order models.

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Hardy Operators on Variable Exponent Spaces

Eigenvalues, Embeddings and Generalised Trigonometric Functions - Lecture Notes in Mathematics ◽

10.1007/978-3-642-18429-1_9 ◽

2011 ◽

pp. 183-209

Author(s):

Jan Lang ◽

David Edmunds

Keyword(s):

Variable Exponent ◽

Variable Exponent Spaces ◽

Hardy Operators

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On Extended General Mittag–Leffler Functions and Certain Inequalities

Fractal and Fractional ◽

10.3390/fractalfract3020032 ◽

2019 ◽

Vol 3 (2) ◽

pp. 32

Author(s):

Marcela V. Mihai ◽

Muhammad Uzair Awan ◽

Muhammad Aslam Noor ◽

Tingsong Du ◽

Artion Kashuri ◽

...

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Fractional Integral Operators ◽

Generalized Fractional Integral ◽

Function Of Two Variables ◽

Generalized Fractional Integral Operators

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.

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Variable Exponent Spaces of Analytic Functions

Advances in Complex Analysis and Applications ◽

10.5772/intechopen.92617 ◽

2020 ◽

Author(s):

Gerardo A. Chacón ◽

Gerardo R. Chacón

Keyword(s):

Hardy Spaces ◽

Measurable Function ◽

Analytic Functions ◽

Variable Exponent ◽

Bergman Spaces ◽

Lebesgue Spaces ◽

Basic Properties ◽

Variable Exponent Spaces ◽

Real Functions ◽

Spaces Of Analytic Functions

Variable exponent spaces are a generalization of Lebesgue spaces in which the exponent is a measurable function. Most of the research done in this topic has been situated under the context of real functions. In this work, we present two examples of variable exponent spaces of analytic functions: variable exponent Hardy spaces and variable exponent Bergman spaces. We will introduce the spaces together with some basic properties and the main techniques used in the context. We will show that in both cases, the boundedness of the evaluation functionals plays a key role in the theory. We also present a section of possible directions of research in this topic.

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Weak Type Estimates of Variable Kernel Fractional Integral and Their Commutators on Variable Exponent Morrey Spaces

Journal of Function Spaces ◽

10.1155/2019/7152346 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

Xukui Shao ◽

Shuangping Tao

Keyword(s):

Lebesgue Space ◽

Variable Exponent ◽

Fractional Integral ◽

Weak Type ◽

Integral Operators ◽

Morrey Spaces ◽

Variable Kernel ◽

Fractional Integral Operators ◽

Weak Type Estimates ◽

Weak Morrey Spaces

In this paper, the authors obtain the boundedness of the fractional integral operators with variable kernels on the variable exponent weak Morrey spaces based on the results of Lebesgue space with variable exponent as the infimum of exponent function p(·) equals 1. The corresponding commutators generated by BMO and Lipschitz functions are considered, respectively.

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