General time-fractional diffusion equation: some uniqueness and existence results for the initial-boundary-value problems

By Yuri Luchko, Masahiro Yamamoto. 2016

159 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c5d03f2d3b48817697e23c9551079ceb8b37e898

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yuri Luchko
2. Masahiro Yamamoto
3. C. Sin
4. Yavar Kian
5. Vasily E. Tarasov
6. Enrique Zuazua
7. Ibtissem Ben Aicha
8. Sylvain Ervedoza

In Modeling and Simulation

1. Yuri Luchko
2. Masahiro Yamamoto
3. C. Sin
4. Yavar Kian
5. Vasily E. Tarasov
6. Bangti Jin

In Numerical Analysis

1. Yuri Luchko
2. Masahiro Yamamoto
3. C. Sin
4. Yavar Kian
5. Vasily E. Tarasov

Citations in the corpus

• The General Fractional Derivative and Related Fractional Differential Equations (2020, methodology): “Then, following [15], the maximum principle is employed to show uniqueness of the strong and the weak solutions to the initial-boundary-value problems for the general time-fractional diffusion equations.”
• On existence and uniqueness of solutions for semilinear fractional wave equations (2015, background): “For 0 α 1, we define ∂αt u by ∂αt u(t, x) := 1 Γ(1−α) ∫ t 0 (t − s)−α∂su(s, x)ds, and there are works in view of the theory of partial differential equations (e.g., Beckers and Yamamoto [1], Luchko [16], Sakamoto and Yamamoto [23], Fujishiro and Kian [3]).”
• Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense (2022, background): “In the next paper [8] devoted to the GFD (11), a maximum principle for the initialboundary-value problems for the time-fractional diffusion equations with the GFD of Caputo type was deduced.”
• Operational Calculus for the General Fractional Derivative and Its Applications (2021, unknown): “Later on, a maximum principle for the initial-boundary-value problems for the general time-fractional diffusion equation in form (7) with a general second order spatial differential operator instead of the Laplace operator ∆ was deduced in [27].”
• General Fractional Integrals and Derivatives with the Sonine Kernels (2021, methodology): “The ordinary fractional differential equations with the Caputo type GFDs are addressed in [1,5–7] and the time-fractional diffusion equations with these derivatives are considered in [1, 3, 5, 8–10].”
• Well-posedness of general Caputo-type fractional differential equations (2018, background): “In the recent paper [15], based on a maximum principle for the general timefractional diffusion equation, the uniqueness results of the strong and the weak solutions were proved.”