Geodesic
Fractional Elliptic Problem With Two Non-Local Terms Involving r(ξ)-Laplacian
Minimax theory and its applications, Tome 10 (2025) no. 1

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In this present paper, we are interested in investigating the existence of weak solutions for a new class of fractional partial differential equations with Laplacian involving the Kirchhoff-type equation in the space fractional , via Mountain Pass Theorem and Ekeland Variational Principle. The idea is to discuss the existence of a weak solution uκ for κ > 0 and a positive solution uκ for κ ∈ (0, κ*) for κ* > 0.
Mots-clés : Fractional Elliptic Equation, ψ-Hilfer Fractional Derivative, Existence of Solutions, Mountain Pass Theorem, Ekeland Variational Principle 
Everson F. S. Feitosa; J. Vanterler C. Sousa; El-Houari Hamza; Arhrrabi Elhoussain. Fractional Elliptic Problem With Two Non-Local Terms Involving r(ξ)-Laplacian. Minimax theory and its applications, Tome 10 (2025) no. 1. http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a6/
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     author = {Everson F. S. Feitosa and J. Vanterler C. Sousa and El-Houari Hamza and Arhrrabi Elhoussain},
     title = {Fractional {Elliptic} {Problem} {With} {Two} {Non-Local} {Terms} {Involving} {r(\ensuremath{\xi})-Laplacian}},
     journal = {Minimax theory and its applications},
     year = {2025},
     volume = {10},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/MTA_2025_10_1_a6/}
}
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