Existence of solutions for a class of boundary value problems involving Riemann Liouville derivative with respect to a function

Abstract

In this article, we study some class of fractional boundary value problem involving generalized Riemann Liouville derivative with respect to a function and the p-Laplace operator. Precisely, using variational methods combined with the mountain pass theorem, we prove that such problem has a nontrivial weak solution. Our main result significantly complement and improves some previous papers in the literature.

Existences Results for Some Nonsingular $p$-Kirchhoff Problems with $\psi$-Hilfer Fractional Derivative

“…So by definition of these manifolds, these solutions are one positive, one negative, and the other change sign. In the case when θ → 0, our problem is reduced to the one studied by Nouf et al [41], and in the case when ψ(x) = x, our problem is reduced to the one studied by Ghanmi and Zhang [15]. We hope to develop other works by considering the singular double-phase problem.…”

“…In the last few years, several authors have concentrated on the study of problems involving the ψ-Riemann fractional derivative, we cite for examples the papers of Alsaedi and Ghanmi [1], Da Sousa et al [26][27][28], Almeida [3], Nouf et al [41], Horrigue [17]. More precisely, Nouf et al [41] used the mountain pass theorem to prove that the following problem…”

Positive, negative, and sign-changing solutions for Kirchhoff problem involving Riemann fractional derivative with respect to a function

“…In the last few years, several authors have been interested in the study of fractional differential equations involving the ψ-Riemann fractional derivative, we cite for examples the papers of Alsaedi and Ghanmi [3], Almeida [2], Guo et al [17], Feng and Sutton [10], Da Sousa et al [38,40,39], Nouf et al [33], Horrigue [21]. More precisely, Nouf et al [33] used the mountain pass theorem to prove that the following problem…”