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

Abstract

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.

A Unified Approach to Solvability and Stability of Multipoint BVPs for Langevin and Sturm–Liouville Equations with CH–Fractional Derivatives and Impulses via Coincidence Theory

“…Rao et al [33] considered the problem of multiplicity of solutions for a mixed H-fractional Laplacian system. Zhao [34,35] thought about the approximation and Hyers-Ulam-type stability of two classes of H-fractional boundary value problems. In [36,37], the authors studied the numerical calculation problem of H-fractional equations.…”

Stability and Numerical Simulation of a Nonlinear Hadamard Fractional Coupling Laplacian System with Symmetric Periodic Boundary Conditions

“…Because it can describe the basic mechanical structure of turbulence problems, many scholars have begun to focus on the dynamics of nonlinear fractional differential equations with the p-Laplacian. In recent years, many excellent results (see [21][22][23][24][25][26]) have been obtained in the study of nonlinear fractional differential equations with the p-Laplacian. For example, Zhao [21] studied a nonlinear Hadamard fractional differential equation with the p-Laplacian.…”

“…In recent years, many excellent results (see [21][22][23][24][25][26]) have been obtained in the study of nonlinear fractional differential equations with the p-Laplacian. For example, Zhao [21] studied a nonlinear Hadamard fractional differential equation with the p-Laplacian. He defined two different distances in a metric space to discuss the solvability, approximation and stability of this system.…”

“…Recently, the study of UH-type stability has still been very popular, especially for fractional-order differential systems. There are many papers dealing with UH-type stability of nonlinear fractional differential systems (see [21,22,25,[29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45], among others). However, the UH-type stability of Hadamard fractional differential coupling systems is rarely studied because the study of the former is much more difficult than that of a single differential equation.…”

Asymptotic Stability and Dependency of a Class of Hybrid Functional Integral Equations

“…Existence and stability results for Atangana-Baleanu fractional problems are established in [16], BVP for a nonlinear Hadamard fractional differential equation is discussed in [17,18], and, for fractional systems, see [19][20][21].…”