Basic Theory of Fractional Differential Equations by Yong Zhou

By Yong Zhou

This precious booklet is dedicated to a quickly constructing sector at the examine of the qualitative idea of fractional differential equations. it's self-contained and unified in presentation, and offers readers the required heritage fabric required to head extra into the topic and discover the wealthy learn literature.

The instruments used comprise many classical and sleek nonlinear research equipment similar to mounted element conception, degree of noncompactness strategy, topological measure procedure, the Picard operators approach, serious element idea and semigroups thought. in accordance with learn paintings performed through the writer and different specialists in past times 4 years, the contents are very new and entire. it truly is worthwhile to researchers and graduate scholars for study, seminars, and complex graduate classes, in natural and utilized arithmetic, physics, mechanics, engineering, biology, and similar disciplines.

Contents:

  • Preliminaries:
    • Introduction
    • Some Notations, suggestions and Lemmas
    • Fractional Calculus
    • Some effects from Nonlinear Analysis
    • Semigroups
  • Fractional useful Differential Equations:
    • Introduction
    • Neutral Equations with Bounded Delay
    • p-Type impartial Equations
    • Neutral Equations with countless Delay
    • Iterative sensible 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 nearly 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 recommendations for BVP with Parameters
    • Infinite recommendations for BVP with Left and correct Fractional Integrals
    • Existence of ideas 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 comparable components of research.

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