Solvability of Fractional Functional Boundary-Value Problems With P-Laplacian Operator on a Half-Line at Resonance

Sun, Bingzhi; Zhang, Shuqin; Jiang, Weihua

doi:10.11948/20210123

Cited by 1 publication

(2 citation statements)

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“…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]).…”

Section: Introductionmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Zhao

2023

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The fractional order p-Laplacian differential equation model is a powerful tool for describing turbulent problems in porous viscoelastic media. The study of such models helps to reveal the dynamic behavior of turbulence. Therefore, this article is mainly concerned with the periodic boundary value problem (BVP) for a class of nonlinear Hadamard fractional differential equation with p-Laplacian operator. By virtue of an important fixed point theorem on a complete metric space with two distances, we study the solvability and approximation of this BVP. Based on nonlinear analysis methods, we further discuss the generalized Ulam-Hyers (GUH) stability of this problem. Eventually, we supply two example and simulations to verify the correctness and availability of our main results. Compared to many previous studies, our approach enables the solution of the system to exist in metric space rather than normed space. In summary, we obtain some sufficient conditions for the existence, uniqueness, and stability of solutions in the metric space.

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