Nonlinear fractional differential equations with integral boundary value conditions

Cabada, Alberto; Hamdi, Zakaria

doi:10.1016/j.amc.2013.11.057

Cited by 100 publications

(71 citation statements)

References 26 publications

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“…Sufficient conditions for the existence of solutions for problem (7.1) were provided in [7]. Before recalling the main result in [7], we need to introduce some notations.…”

Section: Comparison With Existing Resultsmentioning

confidence: 99%

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Positive solutions for a class of fractional boundary value problems with fractional boundary conditions

Azman¹,

Jleli²,

López³

et al. 2018

J. Nonlinear Sci. Appl.

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In this paper, we study the solvability of a nonlinear fractional differential equation under fractional integral boundary conditions. Via a mixed monotone operator method, some new results on the existence and uniqueness of a positive solution for the considered model are obtained. Moreover, we provide iterative sequences for approximating the solution. Some examples are also presented in order to illustrate the obtained result. Keywords:Fractional boundary value problem, fractional integral boundary condition, mixed monotone operator.

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“…Sufficient conditions for the existence of solutions for problem (7.1) were provided in [7]. Before recalling the main result in [7], we need to introduce some notations.…”

Section: Comparison With Existing Resultsmentioning

confidence: 99%

“…In [7], the authors considered the fractional boundary value problem    D α 0 u(t) + F(t, u(t)) = 0, 0 < t < 1, u(0) = u (0) = 0, u(1) = µ . Sufficient conditions for the existence of solutions for problem (7.1) were provided in [7].…”

Section: Comparison With Existing Resultsmentioning

confidence: 99%

Positive solutions for a class of fractional boundary value problems with fractional boundary conditions

Azman¹,

Jleli²,

López³

et al. 2018

J. Nonlinear Sci. Appl.

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show abstract

“…As it has been stated in Sun and Zhao (2014), Zhang (2014), Cabada and Hamdi (2014), Zhao, Chai and Ge (2013), and Jiang and Zhong (2014), this type of conditions appear in different real phenomena, e.g., blood flow problems, chemical engineering, thermoelasticity and population dynamics.…”

Section: Introductionmentioning

confidence: 99%

Existence and non-existence of positive solutions for integral boundary value problems of high-order fractional differential equations with generalised p-Laplacian operator

Sun

Chen

2017

IJDSDE

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Abstract:In this paper, we investigate the non-linear integral boundary value problem of fractional differential equations with generalised p-Laplacian operator. By means of the monotone iteration method, we obtain the existence of positive solutions and establish the iterative sequence for approximating the solutions. Moreover, the non-existence of positive solution is also considered. An example is given to show the applicability of our main results.

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“…Many books on fractional differential equations, fractional calculus have been published (see, for example [15,16,18,21,32]), and some recent papers on the topic, see [1,3,4,5,7,9,11,12,14,19,24,25,26,32] and the references therein. At the same time, there are many papers concerned with solvability of coupled systems of nonlinear fractional differential equations, because of their wide applications.…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions

Zhang¹,

Li²,

Wei³

2016

J. Nonlinear Sci. Appl.

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Nonlinear fractional differential equations with integral boundary value conditions

Cited by 100 publications

References 26 publications

Positive solutions for a class of fractional boundary value problems with fractional boundary conditions

Positive solutions for a class of fractional boundary value problems with fractional boundary conditions

Existence and non-existence of positive solutions for integral boundary value problems of high-order fractional differential equations with generalised p-Laplacian operator

Existence and uniqueness of solutions for a coupled system of nonlinear fractional differential equations with fractional integral boundary conditions

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