Maximum principle for Hadamard fractional differential equations involving fractional Laplace operator

Abstract

The purpose of the current study is to investigate IBVP for spatial‐time fractional differential equation with Hadamard fractional derivative and fractional Laplace operator(−Δ)β. A new Hadamard fractional extremum principle is established. Based on the new result, a Hadamard fractional maximum principle is also proposed. Furthermore, the maximum principle is applied to linear and nonlinear Hadamard fractional equations to obtain the uniqueness and continuous dependence of the solution of the IBVP at hand.

Unique positive solutions for boundary value problem of p-Laplacian fractional differential equation with a sign-changed nonlinearity

“…Because of the extensive application in many fields such as physics, biology and engineering, etc., fractional differential equation has attracted considerable attention and has become an important area of investigation in differential equation theories. For a small sample of such work, we refer the reader to [1][2][3]11,13,16,20] and the references therein. At the same time, the differential equations with p-Laplacian operator are recognized as important mathematical models in various fields of non-Newtonian mechanics, population biology, elasticity theory, and so forth.…”

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“…For application details, we refer the reader to the works presented in [5]- [8]. In particular, there has been shown a great interest in studying a variety of fractional-order boundary value problems, for instance, see [9]- [24]. In the survey paper [25], some interesting results on anti-periodic fractional-order boundary value problems were presented.…”

Existence, uniqueness and stability analysis of a coupled fractional-order differential systems involving Hadamard derivatives and associated with multi-point boundary conditions

“…We refer the reader to [2][3][4][5][6][7][8][9] for details of Hadamard's fractional calculus. In recent years, for example, fractional differential equations involving Hadamard derivatives have attracted considerable attention; see [10][11][12][13][14][15][16][17], and the references cited therein.…”