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Volume 16, Issue 5
The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations

Samah Horrigue, Mona Alsulami & Bayan Abduallah Alsaeedi

DOI: 10.4208/aamm.OA-2022-0009

Adv. Appl. Math. Mech., 16 (2024), pp. 1104-1120.

Published online: 2024-07

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  • Abstract

Using Nehari manifold method combined with fibring maps, we show the existence of nontrivial, weak, positive solutions of the nonlinear $\psi$-Riemann-Liouville fractional boundary value problem involving the $p$-Laplacian operator, given by 

image.png

where $λ>0, 0<\gamma<1< p$ and $\frac{1}{p}<\alpha≤1,$ $g∈C([0,T])$ and $f ∈C^1 ([0,T]×\mathbb{R},\mathbb{R}).$ A useful examples are presented in order to illustrate the validity of our main results.

  • Keywords

$\psi$-Riemann-Liouville fractional derivative, nonlinear fractional differential equations, $p$-Laplacian operator, existence of solutions, Nehari manifold method.

  • AMS Subject Headings

26A33, 34A08, 34B15, 35J20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-16-1104, author = {Horrigue , SamahAlsulami , Mona and Alsaeedi , Bayan Abduallah}, title = {The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2024}, volume = {16}, number = {5}, pages = {1104--1120}, abstract = {

Using Nehari manifold method combined with fibring maps, we show the existence of nontrivial, weak, positive solutions of the nonlinear $\psi$-Riemann-Liouville fractional boundary value problem involving the $p$-Laplacian operator, given by 

image.png

where $λ>0, 0<\gamma<1< p$ and $\frac{1}{p}<\alpha≤1,$ $g∈C([0,T])$ and $f ∈C^1 ([0,T]×\mathbb{R},\mathbb{R}).$ A useful examples are presented in order to illustrate the validity of our main results.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2022-0009}, url = {http://global-sci.org/intro/article_detail/aamm/23287.html} }
TY - JOUR T1 - The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations AU - Horrigue , Samah AU - Alsulami , Mona AU - Alsaeedi , Bayan Abduallah JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 1104 EP - 1120 PY - 2024 DA - 2024/07 SN - 16 DO - http://doi.org/10.4208/aamm.OA-2022-0009 UR - https://global-sci.org/intro/article_detail/aamm/23287.html KW - $\psi$-Riemann-Liouville fractional derivative, nonlinear fractional differential equations, $p$-Laplacian operator, existence of solutions, Nehari manifold method. AB -

Using Nehari manifold method combined with fibring maps, we show the existence of nontrivial, weak, positive solutions of the nonlinear $\psi$-Riemann-Liouville fractional boundary value problem involving the $p$-Laplacian operator, given by 

image.png

where $λ>0, 0<\gamma<1< p$ and $\frac{1}{p}<\alpha≤1,$ $g∈C([0,T])$ and $f ∈C^1 ([0,T]×\mathbb{R},\mathbb{R}).$ A useful examples are presented in order to illustrate the validity of our main results.

Samah Horrigue, Mona Alsulami & Bayan Abduallah Alsaeedi. (2024). The Nehari Manifold for a Class of Singular $\psi$-Riemann-Liouville Fractional with $p$-Laplacian Operator Differential Equations. Advances in Applied Mathematics and Mechanics. 16 (5). 1104-1120. doi:10.4208/aamm.OA-2022-0009
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