Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity

Solvability for the ψ-Caputo-Type Fractional Differential System with the Generalized p-Laplacian Operator

“…As a popular research object in recent years, fractional differential equations (FDEs) play an important role in modeling many practical problems of science and engineering, such as fluid flow, anomalous diffusion, viscoelastic mechanics, epidemiology, etc. (see [1][2][3][4][5][6]). There are various definitions of fractional integration and differentiation, including the most widely used classical definitions of Riemann-Liouville, Caputo, Hadamard and others (see [7][8][9][10]).…”

On critical variable-order Kirchhoff type problems with variable singular exponent

“…Canino et al [8] generalized the result by Chen et al [10,Section 3] to the case of p-fractional Laplacian (−∆ p ) s . We draw the attention of the reader to [1,17] (not restricted to only these) for existence results and [15,29,30,36,38] for the multiplicity results. Off-late, from a scientific point of view, fractional Sobolev spaces and related non-local problems have attracted the attention of many scholars because they occur naturally in many fields, such as electrorheological fluids and image processing (cf.…”

“…Readers who are interested to know the physical motivation behind the study of elliptic problems involving Kirchhoff operator can refer to Carrier [9]. In fact, there are only a few papers on the p(x)-Laplace operator involving singular nonlinearity and some of which can be found in the articles [2,17] and the references therein.…”