Existence of Solutions for a Singular Double Phase Problem Involving a $$\psi $$-Hilfer Fractional Operator Via Nehari Manifold

Existence of Weak Solutions for the Class of Singular Two-Phase Problems with a ψ-Hilfer Fractional Operator and Variable Exponents

“…The existence of solutions for a singular double-phase problem involving a ψ-Hilfer fractional operator has been established through the utilization of the Nehari manifold [23]. In the reference [24], Ezati and Nyamoradi, using the genus properties of critical point theory, studied the existence and multiplicity of solutions of the Kirchhoff equation ψ-Hilfer fractional operator p−Laplacian.…”

“…Many models of fractional differential equations have been worked on by researchers using variational problems that include fractional operators: for example, Nyamoradi and Tayyebi [25], Ghanmi and Zhang [26], Kamache et al [27], and Sousa et al [21,23]. For example, in [27], Kamache et al discussed a class of perturbed nonlinear fractional p-Laplacian differential systems and proved the existence of three weak solutions by using the variational method and Ricceri's critical point theorems.…”

“…For example, in [27], Kamache et al discussed a class of perturbed nonlinear fractional p-Laplacian differential systems and proved the existence of three weak solutions by using the variational method and Ricceri's critical point theorems. On the other hand, in [23], Sousa et al investigated a new class of two-phase single p-Laplacian equation problems with a fractional ψ-Hilfer operator incorporated from a parametric term. Using the fiber method with a Nehari manifold, they proved that there are at least two weak solutions to such problems when the parameter is small enough.…”