Nonlinear Langevin equations and inclusions involving mixed fractional order derivatives and variable coefficient with fractional nonlocal-terminal conditions

被引：13

作者：

Ahmad, Bashir ^{[1
]}

Alsaedi, Ahmed ^{[1
]}

Ntouyas, Sotiris K. ^{[1
,2
]}

机构：

[1] King Abdulaziz Univ, Fac Sci, Dept Math, Nonlinear Anal & Appl Math NAAM Res Grp, POB 80203, Jeddah 21589, Saudi Arabia

[2] Univ Ioannina, Dept Math, Ioannina 45110, Greece

来源：

AIMS MATHEMATICS | 2019年 / 4卷 / 03期

关键词：

fractional derivatives; fractional integral; Langevin equations; nonlocal terminal value problems; existence; uniqueness; fixed point theorems; DIFFERENTIAL-EQUATIONS; EXISTENCE;

D O I：

10.3934/math.2019.3.626

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we discuss the existence and uniqueness of solutions for a new kind of Langevin equation involving Riemann-Liouville as well as Caputo fractional derivatives, and variable coefficient, supplemented with nonlocal-terminal fractional integro-differential conditions. The proposed study is based on modem tools of functional analysis. We also extend our discussion to the associated inclusions problem. For the applicability of the obtained results, several examples are constructed. Some interesting observations are also presented.

引用

页码：626 / 647

页数：22

共 30 条

[21]

LASOTA A, 1965, B ACAD POL SCI SMAP, V13, P781

[22] Modeling the transition between stable and unstable operation while emptying a silo [J].

Leszczynski, J. S. ;

Blaszczyk, T. .

GRANULAR MATTER, 2011, 13 (04) :429-438

[23] Langevin equation with two fractional orders [J].

Lim, S. C. ;

Li, Ming ;

Teo, L. P. .

PHYSICS LETTERS A, 2008, 372 (42) :6309-6320

[24]

Miller Kenneth S, 1993, An introduction to the fractional calculus and fractional differential equations

[25]

Podlubny I., 1999, Fractional Differential Equations

[26] EXISTENCE THEOREMS FOR SEMI-LINEAR CAPUTO FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL DISCRETE AND INTEGRAL BOUNDARY CONDITIONS [J].

Qarout, Doa'a ;

Ahmad, Bashir ;

Alsaedi, Ahmed .

FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2016, 19 (02) :463-479

[27]

Samko S. G., 1993, Fractional integrals and derivatives. Theory and applications, DOI DOI 10.1007/S10957-022-02125-9

[28] Nonlinear Langevin Equation of Hadamard-Caputo Type Fractional Derivatives with Nonlocal Fractional Integral Conditions [J].

Tariboon, Jessada ;

Ntouyas, Sotiris K. ;

Thaiprayoon, Chatthai .

ADVANCES IN MATHEMATICAL PHYSICS, 2014, 2014

[29] Generalized Langevin equation revisited: mechanical random force and self-consistent structure [J].

Uranagase, Masayuki ;

Munakata, Toyonori .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (45)

[30] Existence of fractional differential equations [J].

Yu, C ;

Gao, GZ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 310 (01) :26-29

← 1 2 3 →