Solvability of boundary value problems of nonlinear fractional differential equations

Chen, Weiqi; Zhao, Yige

doi:10.1186/s13662-015-0373-2

Cited by 4 publications

(3 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[2][3][4][5][6][7][8][9][10][11][12]. For some recent developments regarding this, and in particular, fractional Langevin equations, see [13][14][15][16][17][18][19][20][21][22][23] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Salem

Alnegga

2020

Axioms

View full text Add to dashboard Cite

In this research article, we introduce a new class of hybrid Langevin equation involving two distinct fractional order derivatives in the Caputo sense and Riemann–Liouville fractional integral. Supported by three-point boundary conditions, we discuss the existence of a solution to this boundary value problem. Because of the important role of the measure of noncompactness in fixed point theory, we use the technique of measure of noncompactness as an essential tool in order to get the existence result. The modern analysis technique is used by applying a generalized version of Darbo’s fixed point theorem. A numerical example is presented to clarify our outcomes.

show abstract

Section: Introductionmentioning

confidence: 99%

Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Salem

Alnegga

2020

Axioms

View full text Add to dashboard Cite

show abstract

“…Much attention is paid to the investigation of the existence and multiplicity of positive solutions for boundary value problems of fractional differential equations by applying different techniques from nonlinear analysis (fixed-point theorems [16,26,29,31], upper and lower solutions method [11,22], fixed-point index theory [32], etc. ).…”

Section: Introductionmentioning

confidence: 99%

Green's functions for boundary value problems of generalized fractional differential equations with p-Laplacian

Seemab

Rehman

2020

Hacettepe Journal of Mathematics and Statistics

View full text Add to dashboard Cite

We utilize the recently presented generalized fractional derivatives, which are not the same as standard Caputo and Riemann-Liouville fractional derivatives, to reformulate some boundary value problems of fractional differential equations. For some classes of generalized fractional differential equations with boundary conditions build up, we find the corresponding Green's functions and establish their properties under suitable assumptions and we also demonstrate the applicability of these properties of the Green's functions to establish some existence results via fixed point theorems.

show abstract

“…[13,14,15,16]. Boundary-value problems for fractional differential equations have been discussed in [4,5,6,8,10]. In [9], the authors have investigated the existence and uniqueness of solutions for Langevin equation with two fractional orders.…”

Section: Introductionmentioning

confidence: 99%

The Existence and Uniqueness of Solutions for a Nonlinear Fractional Caputo-Langevin Equation With Multi-Point Boundary Conditions

Adjeroud¹

2017

Int. J. of Pure and Appl. Math.

View full text Add to dashboard Cite

show abstract

Solvability of boundary value problems of nonlinear fractional differential equations

Abstract: In this paper, we study the existence of multiple positive solutions for the nonlinear fractional differential equation boundary value problem

Cited by 4 publications

References 21 publications

Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Measure of Noncompactness for Hybrid Langevin Fractional Differential Equations

Green's functions for boundary value problems of generalized fractional differential equations with p-Laplacian

The Existence and Uniqueness of Solutions for a Nonlinear Fractional Caputo-Langevin Equation With Multi-Point Boundary Conditions

Contact Info

Product

Resources

About