Multiple Positive Solutions for Fractional Three-Point Boundary Value Problem with <i>p</i>-Laplacian Operator

Dong, Lixue; Liu, Yang; Wang, Chunli

doi:10.1155/2020/2327580

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…Overall, we believe that tripled fractional order systems have the potential to make a significant impact on a wide range of industries and scientific disciplines. For further insights into the applications of fractional calculus in various fields and related literature on positive solutions with different boundary conditions, we recommend reading the referenced books [32][33][34] and exploring the cited papers [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53].…”

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confidence: 99%

Multiple Positive Solutions for a System of Fractional Order BVP with p-Laplacian Operators and Parameters

Ahmadini,

Khuddush,

Nageswara Rao

2023

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In this paper, we investigate the existence of positive solutions to a system of fractional differential equations that include the (r1,r2,r3)-Laplacian operator, three-point boundary conditions, and various fractional derivatives. We use a combination of techniques, including cone expansion and compression of the functional type, and the Leggett–Williams fixed point theorem, to prove the existence of positive solutions. Finally, we provide two examples to illustrate our main results.

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confidence: 99%

Multiple Positive Solutions for a System of Fractional Order BVP with p-Laplacian Operators and Parameters

Ahmadini,

Khuddush,

Nageswara Rao

2023

Axioms

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Multiple Positive Solutions for a Coupled System of Fractional Order BVP with p-Laplacian Operators and Parameters

Ahmadini,

Khuddush,

Nageswara Rao

2023

Preprint

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In this study, we investigate the existence of positive solutions within a system of Riemann-Liouville fractional differential equations that incorporate the (r1,r2,r3)-Laplacian operator while being subject to three-point boundary conditions. These equations incorporate various fractional derivatives and are influenced by parameters represented as (ψ1,ψ2,ψ3). Our approach involves employing techniques such as cone expansion and compression of the functional type, in conjunction with the Leggett-Williams fixed point theorem, to establish the existence of positive solutions. To emphasize the practical significance of our findings in the realm of fractional differential equations, we provide two illustrative examples.

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Positive solutions for a system of Hadamard fractional $ (\varrho_{1}, \varrho_{2}, \varrho_{3}) $-Laplacian operator with a parameter in the boundary

Msmali

2022

MATH

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<abstract><p>In this paper, we are gratified to explore existence of positive solutions for a tripled nonlinear Hadamard fractional differential system with $ (\varrho_{1}, \varrho_{2}, \varrho_{3}) $-Laplacian operator in terms of the parameter $ (\sigma_{1}, \sigma_{2}, \sigma_{3}) $ are obtained, by applying Avery-Henderson and Leggett-Williams fixed point theorems. As an application, an example is given to illustrate the effectiveness of the main result.</p></abstract>

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Multiple Positive Solutions for Fractional Three-Point Boundary Value Problem with p-Laplacian Operator

Cited by 3 publications

References 13 publications

Multiple Positive Solutions for a System of Fractional Order BVP with p-Laplacian Operators and Parameters

Multiple Positive Solutions for a System of Fractional Order BVP with p-Laplacian Operators and Parameters

Multiple Positive Solutions for a Coupled System of Fractional Order BVP with p-Laplacian Operators and Parameters

Positive solutions for a system of Hadamard fractional $ (\varrho_{1}, \varrho_{2}, \varrho_{3}) $-Laplacian operator with a parameter in the boundary

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