On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions

Henderson, Johnny; Luca, Rodica; Tudorache, Alexandru

doi:10.1515/fca-2015-0024

Cited by 99 publications

(47 citation statements)

References 10 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 literature on the topic includes the existence and uniqueness results related to classical, periodic/anti-periodic, nonlocal, multi-point, and integral boundary conditions, for instance, see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Existence theory for fractional differential equations with non-separated type nonlocal multi-point and multi-strip boundary conditions

et al. 2018

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We introduce a more general class of fractional-order boundary value problems involving non-separated type multi-point and multi-strip boundary conditions. Several existence and uniqueness results for the given problem are established by applying the tools of fixed-point theory. Some illustrative examples are also included. The boundary conditions introduced in this work are of quite general nature and reduce to many special cases by fixing the parameters involved in the conditions.

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“…For some recent results on positive solutions of fractional differential equations we refer to [32]- [37] and references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

et al. 2017

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On a System of Fractional Differential Equations with Coupled Integral Boundary Conditions

Abstract: We investigate the existence and multiplicity of positive solutions for a system of nonlinear Riemann-Liouville fractional differential equations, subject to coupled integral boundary conditions. The nonsingular and singular cases are studied.

Cited by 99 publications

References 10 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

Existence theory for fractional differential equations with non-separated type nonlocal multi-point and multi-strip boundary conditions

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

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