Fractional Differential Equations

1. Front Matter

   Pages i-xiv

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2. Preliminaries

   1. Front Matter

      Pages 1-1

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   2. Continuous Time Random Walk

      • Bangti Jin

      Pages 3-18

   3. Fractional Calculus

      • Bangti Jin

      Pages 19-58

   4. Mittag-Leffler and Wright Functions

      • Bangti Jin

      Pages 59-94

3. Fractional Ordinary Differential Equations

   1. Front Matter

      Pages 95-95

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   2. Cauchy Problem for Fractional ODEs

      • Bangti Jin

      Pages 97-136

   3. Boundary Value Problem for Fractional ODEs

      • Bangti Jin

      Pages 137-172

4. Time-Fractional Diffusion

   1. Front Matter

      Pages 173-173

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   2. Subdiffusion: Hilbert Space Theory

      • Bangti Jin

      Pages 175-276

   3. Subdiffusion: Hölder Space Theory

      • Bangti Jin

      Pages 277-330

5. Back Matter

   Pages 331-368

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This graduate textbook provides a self-contained introduction to modern mathematical theory on fractional differential equations. It addresses both ordinary and partial differential equations with a focus on detailed solution theory, especially regularity theory under realistic assumptions on the problem data. The text includes an extensive bibliography, application-driven modeling, extensive exercises, and graphic illustrations throughout to complement its comprehensive presentation of the field. It is recommended for graduate students and researchers in applied and computational mathematics, particularly applied analysis, numerical analysis and inverse problems.

• Fractional calculus
• Fractional differential equation
• time-fractional diffusion
• Mittag-Leffler Function
• regularity
• well-posedness
• inverse problems
• ordinary differential equations
• Fractional ODEs
• Hilbert Space Theory
• Fractional Laplacian
• Wright function

• Department of Computer Science, University College London, London, UK

  Bangti Jin

Bangti Jin received the B.Eng. degree in polymeric materials and engineering in 2002, theM.Sc. degree in computational mathematics in 2005, both from Zhejiang University, Hangzhou, China, and the Ph.D. degree in applied mathematics from the Chinese University of Hong Kong, Hong Kong, in 2008. Previously, he was an Assistant Professor of mathematics at the University of California, Riverside (2013–2014), a Visiting Assistant Professor at Texas A&M University (2010–2013), an Alexandre von Humboldt Postdoctoral Researcher at the University of Bremen (2009–2010). He is currently Professor of Inverse Problems at the Department of Computer Science, University College London, London, U.K. His research interests include computational inverse problems and numerical analysis of differential equations.

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