New PDF release: Basic Theory of Fractional Differential Equations

By Yong Zhou

This priceless booklet is dedicated to a swiftly constructing region at the learn of the qualitative idea of fractional differential equations. it's self-contained and unified in presentation, and offers readers the mandatory history fabric required to head extra into the topic and discover the wealthy study literature.

The instruments used contain many classical and sleek nonlinear research equipment corresponding to mounted element thought, degree of noncompactness technique, topological measure procedure, the Picard operators procedure, severe aspect conception and semigroups concept. in keeping with study paintings conducted by way of the writer and different specialists in the past 4 years, the contents are very new and finished. it really is worthwhile to researchers and graduate scholars for examine, seminars, and complicated graduate classes, in natural and utilized arithmetic, physics, mechanics, engineering, biology, and comparable disciplines.

Contents:

  • Preliminaries:
    • Introduction
    • Some Notations, options and Lemmas
    • Fractional Calculus
    • Some effects from Nonlinear Analysis
    • Semigroups
  • Fractional practical Differential Equations:
    • Introduction
    • Neutral Equations with Bounded Delay
    • p-Type impartial Equations
    • Neutral Equations with limitless Delay
    • Iterative useful 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 price difficulties through severe element 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 options 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 parts of research.

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