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

Author

Listed:
  • Binh Duy Ho
  • Van Kim Ho Thi
  • Long Le Dinh
  • Nguyen Hoang Luc
  • Phuong Nguyen

Abstract

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.

Suggested Citation

  • Binh Duy Ho & Van Kim Ho Thi & Long Le Dinh & Nguyen Hoang Luc & Phuong Nguyen, 2021. "On Fractional Diffusion Equation with Caputo‐Fabrizio Derivative and Memory Term," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).
    • Handle: RePEc:wly:jnlamp:v:2021:y:2021:i:1:n:9259967
    DOI: 10.1155/2021/9259967
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    1. Korpinar, Zeliha & Inc, Mustafa & Bayram, Mustafa, 2020. "Theory and application for the system of fractional Burger equations with Mittag leffler kernel," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    2. Acay, Bahar & Inc, Mustafa, 2021. "Fractional modeling of temperature dynamics of a building with singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Erdal Karapınar & Andreea Fulga & Maliha Rashid & Lariab Shahid & Hassen Aydi, 2019. "Large Contractions on Quasi-Metric Spaces with an Application to Nonlinear Fractional Differential Equations," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    4. Singh, Jagdev, 2020. "Analysis of fractional blood alcohol model with composite fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Yusuf, Abdullahi & Acay, Bahar & Mustapha, Umar Tasiu & Inc, Mustafa & Baleanu, Dumitru, 2021. "Mathematical modeling of pine wilt disease with Caputo fractional operator," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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