Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator

Nguyen Hoang Luc; Donal O’Regan; Anh Tuan Nguyen

doi:10.3390/fractalfract6090530

Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator

Nguyen Hoang Luc, Donal O’Regan, Anh Tuan Nguyen

Mathematics

Thu Dau Mot University

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

1 Citation (Scopus)

Abstract

We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces.

Original language	English
Article number	530
Journal	Fractal and Fractional
Volume	6
Issue number	9
DOIs	https://doi.org/10.3390/fractalfract6090530
Publication status	Published - Sep 2022

Keywords

fractional diffusion equation
fractional partial differential equations
gradient nonlinearity
hyper-Bessel

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abstract = "We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces.",

keywords = "fractional diffusion equation, fractional partial differential equations, gradient nonlinearity, hyper-Bessel",

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AU - O’Regan, Donal

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N2 - We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces.

AB - We investigate the Cauchy problem for a nonlinear fractional diffusion equation, which is modified using the time-fractional hyper-Bessel derivative. The source function is a gradient source of Hamilton–Jacobi type. The main objective of our current work is to show the existence and uniqueness of mild solutions. Our desired goal is achieved using the Picard iteration method, and our analysis is based on properties of Mittag–Leffler functions and embeddings between Hilbert scales spaces and Lebesgue spaces.

KW - fractional diffusion equation

KW - fractional partial differential equations

KW - gradient nonlinearity

KW - hyper-Bessel

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ER -

Solutions of a Nonlinear Diffusion Equation with a Regularized Hyper-Bessel Operator

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