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Journal of Applied Nonlinear Dynamics 11(4) (2022) 789--803 | DOI:10.5890/JAND.2022.12.002

Fares Kamache$^{1}$, Rafik Guefaifia$^{2}$, Salah Boulaaras$^{3}$

$^{1}$ Laboratory of Mathematics, Informatics and systemes (LAMIS), Larbi Tebessi University -Tebessa, Algeria

$^{2}$ Department of Mathematics, College of Sciences and Arts, Al-Rass, Qassim University, Kingdom of Saudi Arabia

$^{3}$ Laboratory of Fundamental and Applied Mathematics of Oran (LMFAO), University of Oran 1, Ahmed Benbella, Algeria

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Abstract

In this work, it is proved the existence of at least three weak solutions can be obtained for a new class of nonlinear fractional boundary value systems by using variational methods combined with a critical point theory due to Bonano and Marano while two examples in $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{3}$ and $% %TCIMACRO{\U{211d} }% %BeginExpansion \mathbb{R} %EndExpansion ^{4}$ are given to illustrate our main results applications.

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