Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions

Ahmad, Bashir; Alsaedi, Ahmed; Alghamdi, Badra S.

doi:10.1016/j.nonrwa.2007.05.005

Cited by 142 publications

(80 citation statements)

References 36 publications

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“…Multi-point boundary conditions and integral boundary conditions become hot spots of research among different types of boundary value problems, and the studies in [5][6][7][8][9] are excellent. However, most researchers tend to investigate either integral conditions or multi-point conditions.…”

Section: Introductionmentioning

confidence: 99%

Existence results for fractional differential equations with integral and multi-point boundary conditions

2018

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This paper concerns a new kind of fractional differential equation of arbitrary order by combining a multi-point boundary condition with an integral boundary condition. By solving the equation which is equivalent to the problem we are going to investigate, the Green's functions are obtained. By defining a continuous operator on a Banach space and taking advantage of the cone theory and some fixed point theorems, the existence of multiple positive solutions for the BVPs is proved based on some properties of Green's functions and under the circumstance that the continuous functions f satisfy certain hypothesis. Finally, examples are provided to illustrate the results.

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Section: Introductionmentioning

confidence: 99%

Existence results for fractional differential equations with integral and multi-point boundary conditions

2018

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“…The motivation of a such study is due to the importance and numerous applications of integral boundary conditions in different fields, such as blood flow problems, chemical engineering, thermo-elasticity, etc. See, for example [2,11,24,25].…”

Section: Introductionmentioning

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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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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“…The existence and multiplicity of positive solutions for such problems have received a great deal of attentions. To indentify a few, we refer the reader to [1,2,8,13,19,23,24] and references therein. On the other hand, there are fewer results in the literature for higher-order differential equations with integral boundary conditions, see [3,4,20].…”

Section: Introductionmentioning

confidence: 99%

Positive solutions of nth-order impulsive differential equations with integral boundary conditions

Fen

Karaca

2016

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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Analytic approximation of solutions of the forced Duffing equation with integral boundary conditions

Cited by 142 publications

References 36 publications

Existence results for fractional differential equations with integral and multi-point boundary conditions

Existence results for fractional differential equations with integral and multi-point boundary conditions

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

Positive solutions of nth-order impulsive differential equations with integral boundary conditions

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