On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term | Zendy

Binh Duy Ho | Zendy; Van Kim Ho Thi | Zendy; Le Dinh Long | Zendy; Nguyen Hoang Luc | Zendy; Nguyen Duc Phuong | Zendy

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On Fractional Diffusion Equation with Caputo-Fabrizio Derivative and Memory Term

Author(s) -

Binh Duy Ho,

Van Kim Ho Thi,

Le Dinh Long,

Nguyen Hoang Luc,

Nguyen Duc Phuong

Publication year - 2021

Publication title -

advances in mathematical physics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.283

H-Index - 23

eISSN - 1687-9139

pISSN - 1687-9120

DOI - 10.1155/2021/9259967

Subject(s) - uniqueness , mathematics , fractional calculus , fixed point theorem , embedding , sobolev space , term (time) , banach fixed point theorem , banach space , hilbert space , mathematical analysis , diffusion , derivative (finance) , pure mathematics , computer science , physics , quantum mechanics , financial economics , economics , thermodynamics , artificial intelligence

In this paper, we examine a nonlinear fractional diffusion equation containing viscosity terms with derivative in the sense of Caputo-Fabrizio. First, we establish the local existence and uniqueness of lightweight solutions under some assumptions about the input data. Then, we get the global solution using some new techniques. Our main idea is to combine theories of Banach’s fixed point theorem, Hilbert scale theory of space, and some Sobolev embedding.

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