Basic Theory of Fractional Differential Equations by Yong Zhou

By Yong Zhou

This worthwhile booklet is dedicated to a quickly constructing quarter at the learn of the qualitative thought of fractional differential equations. it's self-contained and unified in presentation, and offers readers the required historical past fabric required to move extra into the topic and discover the wealthy study literature.

The instruments used comprise many classical and sleek nonlinear research tools similar to mounted element concept, degree of noncompactness procedure, topological measure process, the Picard operators procedure, severe element concept and semigroups thought. in accordance with learn paintings conducted via the writer and different specialists up to now 4 years, the contents are very new and finished. it's necessary to researchers and graduate scholars for study, seminars, and complicated graduate classes, in natural and utilized arithmetic, physics, mechanics, engineering, biology, and similar disciplines.


  • Preliminaries:
    • Introduction
    • Some Notations, recommendations and Lemmas
    • Fractional Calculus
    • Some effects from Nonlinear Analysis
    • Semigroups
  • Fractional sensible Differential Equations:
    • Introduction
    • Neutral Equations with Bounded Delay
    • p-Type impartial Equations
    • Neutral Equations with endless Delay
    • Iterative practical Differential Equations
    • Notes and Remarks
  • Fractional usual Differential Equations in Banach Spaces:
    • Introduction
    • Cauchy difficulties through degree of Noncompactness Method
    • Cauchy difficulties through Topological measure Method
    • Cauchy difficulties through Picard Operators Technique
    • Notes and Remarks
  • Fractional summary Evolution Equations:
    • Introduction
    • Evolution Equations with Riemann-Liouville Derivative
    • Evolution Equations with Caputo Derivative
    • Nonlocal Cauchy difficulties for Evolution Equations
    • Abstract Cauchy issues of virtually Sectorial Operators
    • Notes and Remarks
  • Fractional Boundary worth difficulties through serious aspect Theory:
    • Introduction
    • Existence of resolution for BVP with Left and correct Fractional Integrals
    • Multiple ideas for BVP with Parameters
    • Infinite strategies for BVP with Left and correct Fractional Integrals
    • Existence of suggestions for BVP with Left and correct Fractional Derivatives
    • Notes and Remarks
  • Fractional Partial Differential Equations:
    • Introduction
    • Fractional Euler-Lagrange Equations
    • Time-Fractional Diffusion Equations
    • Fractional Hamiltonian Systems
    • Fractional Schrödinger Equations
    • Notes and Remarks

Readership: Graduate scholars and researchers within the fields of fractional differential equations, fractional calculus and similar parts of research.

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