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Existence and multiplicity of solutions to a ψ-Hilfer fractional p-Laplacian equations.
- Source :
- Asian-European Journal of Mathematics; Mar2023, Vol. 16 Issue 3, p1-15, 15p
- Publication Year :
- 2023
-
Abstract
- In this paper, by Symmetric Mountain Pass Lemma, we study the existence and multiplicity of solutions to the following nonlocal ψ -Hilfer fractional p -Laplasian equation: H D T α , β ; ψ (| H D 0 + α , β ; ψ ξ (x) | p − 2 H D 0 + α , β ; ψ ξ (x)) − γ (x) | ξ (x) | r − 2 ξ (x) − g (x , ξ (x)) = 0 , I 0 + β (β − 1) ; ψ ξ (0) = I T β (β − 1) ; ψ ξ (T) = 0 , where H D 0 + α , β ; ψ ξ (x) and H D T α , β ; ψ are ψ -Hilfer fractional derivatives left-sided and right-sided of order 1 p < α < 1 , 0 ≤ β ≤ 1 , r > p and I 0 + β (β − 1) ; ψ (.) and I T β (β − 1) ; ψ (.) are ψ -Riemann–Liouville fractional integrals left-sided and right-sided, γ : [ 0 , T ] → ℝ and g : [ 0. T ] × ℝ → ℝ are continuous functions. Finally, we give some examples to illustrate the main results. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 17935571
- Volume :
- 16
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Asian-European Journal of Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 161723850
- Full Text :
- https://doi.org/10.1142/S1793557123500456