Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions

Tariboon, Jessada; Ntouyas, Sotiris K.; Thaiprayoon, Chatthai

doi:10.1155/2014/372749

Cited by 28 publications

(8 citation statements)

References 27 publications

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“…ere is a clear progress on fractional Langevin equations in physics (see [21,22]). New results on Langevin equations under the variety of boundary value conditions have been published [23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

Salem

Alzahrani

Alnegga

2020

Mathematical Problems in Engineering

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is research paper is about the existence and uniqueness of the coupled system of nonlinear fractional Langevin equations with multipoint and nonlocal integral boundary conditions. e Caputo fractional derivative is used to formulate the fractional differential equations, and the fractional integrals mentioned in the boundary conditions are due to Atangana-Baleanu and Katugampola. e existence of solution has been proven by two main fixed-point theorems: O'Regan's fixed-point theorem and Krasnoselskii's fixed-point theorem. By applying Banach's fixed-point theorem, we proved the uniqueness result for the concerned problem. is research paper highlights the examples related with theorems that have already been proven. HindawiMathematical Problems in Engineering Volume 2020, Article ID 7345658, 15 pages https://doi.org/10.1155/2020/7345658

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Section: Introductionmentioning

confidence: 99%

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

Salem

Alzahrani

Alnegga

2020

Mathematical Problems in Engineering

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“…Fractional derivative arises from many physical processes, such as a charge transport in amorphous semiconductors [22], electrochemistry and material science, they are in fact described by differential equations of fractional order [9,10,17,18]. Recently, many studies on fractional differential equations, involving different operators such as Riemann-Liouville operators [19,24], Caputo operators [1,3,13,25], Hadamard operators [23] and q−fractional operators [2], have appeared during the past several years. Moreover, by applying different techniques of nonlinear analysis, many authors have obtained results of the existence and uniqueness of solutions for various classes of fractional differential equations, for example, we refer the reader to [3-8, 11, 12, 14, 15, 19] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders

Houas¹

2018

ATA

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In this work, we study existence and uniqueness of solutions for multi-point boundary value problem of nonlinear fractional differential equations with two fractional derivatives. By using the variety of fixed point theorems, such as Banach's fixed point theorem, Leray-Schauder's nonlinear alternative and Leray-Schauder's degree theory, the existence of solutions is obtained. At the end, some illustrative examples are discussed.

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“…For some new developments on the fractional Langevin equation, see, for example, [3,5,10,[18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions

Sitho¹,

Laoprasittichok²,

Ntouyas³

et al. 2016

J. Nonlinear Sci. Appl.

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In the present paper, we study a new class of boundary value problems for Langevin quantum difference equations with multi-quantum numbers q-derivative nonlocal conditions. Some new existence and uniqueness results are obtained by using standard fixed point theorems. The existence and uniqueness of solutions is established by Banach's contraction mapping principle, while the existence of solutions is derived by using Krasnoselskii's fixed point theorem and Leray-Schauder's nonlinear alternative. Examples illustrating the results are also presented.

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Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions

Cited by 28 publications

References 27 publications

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

Coupled System of Nonlinear Fractional Langevin Equations with Multipoint and Nonlocal Integral Boundary Conditions

Existence of Solutions for Fractional Differential Equations Involving Two Riemann-Liouville Fractional Orders

Quantum difference Langevin equation with multi-quantum numbers q-derivative nonlocal conditions

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