On a multi‐point p$$ p $$‐Laplacian fractional differential equation with generalized fractional derivatives

Abstract

In the current paper, we intend to check the existence aspects of solutions for a category of the multi-point boundary value problem (BVP) involving a p-Laplacian differential operator within the generalized fractional derivatives depending on another function. Based on two fixed point results attributed to Schaefer and Banach, the desired results are verified. Further, the continuity of solutions in terms of inputs (fractional orders, associated parameters, and appropriate function) is extensively discussed. A simulative example is prepared to demonstrate the applications of the obtained results.

Solvability, Approximation and Stability of Periodic Boundary Value Problem for a Nonlinear Hadamard Fractional Differential Equation with p-Laplacian

“…In [4], based on the Guo-Krasnosel'skii fixed point theorem, the authors probed into the multiple positive solutions of a system of mixed Hadamard fractional BVP with (p 1 , p 2 )-Laplacian. In fact, some articles have been disposed of the BVP of p-Laplacian system involving Riemann-Liouville or Caputo fractional derivatives (see [5][6][7][8][9][10][11][12][13]).…”

“…In addition, we build the generalized Ulam-Hyers stability of system (1) based on nonlinear analysis methods and inequality techniques. (c) Many previous papers (see [2][3][4][5][6][7][8][9][10][11][12][13][17][18][19]24,25]) usually used some fixed-point theorems on Banach spaces to study the existence of solutions of fractional differential equations. However, we handle the existence of solutions to fractional order differential equations by defining two different distances on a complete distance space.…”

On the Solvability of Equations with a Distributed Fractional Derivative Given by the Stieltjes Integral

“…Equations with fractional derivatives of various forms attract the attention of researchers both from a theoretical point of view and because of their widespread use in applied problems, see, e.g., recent papers [1][2][3] and many other works. The distributed derivatives (other names are continual derivatives [4], mean derivatives [5]) are used for the investigation of some real phenomena and processes when an order of a fractional derivative in a model continuously depends on the process parameters: in the theory of viscoelasticity [5], in modeling dielectric induction and diffusion [6,7], in the kinetic theory [8], and in other scientific fields [4,[9][10][11][12].…”

“…The second section contains the study of the properties of some analytic functions, which are associated with an integral from Equation (1). Then the notion of a k-resolving family, k = 0, 1, .…”

On the Boundary Value Problem of Nonlinear Fractional Integro-Differential Equations

“…In 2022, Rezapour et al [14] investigated the existence of solutions for a category of the multi-point boundary value problem involving a p-Laplacian differential operator with the generalized fractional derivatives depending on another function. The authors in [15] considered the existence, uniqueness and stability of a positive solution in relation to a fractional version of a variable order thermostat model equipped with nonlocal boundary values in the Caputo sense using Guo-Krasnoselskii's fixed point theorem on cones.…”