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.

Contents:

  • 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.

Show description

Read Online or Download Basic Theory of Fractional Differential Equations PDF

Similar differential equations books

Dynamics of Third-Order Rational Difference Equations with Open Problems and Conjectures (Advances in Discrete Mathematics and Applications)

Extending and generalizing the result of rational equations, Dynamics of 3rd Order Rational distinction Equations with Open difficulties and Conjectures makes a speciality of the boundedness nature of suggestions, the worldwide balance of equilibrium issues, the periodic personality of ideas, and the convergence to periodic strategies, together with their periodic trichotomies.

Rate-Independent Systems: Theory and Application (Applied Mathematical Sciences)

This monograph offers either an creation to and an intensive exposition of the idea of rate-independent platforms, which the authors were engaged on with loads of collaborators over 15 years. the point of interest is generally on totally rate-independent platforms, first on an summary point both with or perhaps with no linear constitution, discussing a number of recommendations of ideas with complete mathematical rigor.

Handbook of Linear Partial Differential Equations for Engineers and Scientists, Second Edition

Contains approximately 4,000 linear partial differential equations (PDEs) with solutionsPresents recommendations of various difficulties suitable to warmth and mass move, wave concept, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction idea, quantum mechanics, chemical engineering sciences, electric engineering, and different fieldsOutlines uncomplicated tools for fixing numerous difficulties in technology and engineeringContains even more linear equations, difficulties, and strategies than the other ebook at the moment availableProvides a database of try difficulties for numerical and approximate analytical tools for fixing linear PDEs and platforms of coupled PDEsNew to the second one EditionMore than seven-hundred pages with 1,500+ new first-, second-, third-, fourth-, and higher-order linear equations with solutionsSystems of coupled PDEs with solutionsSome analytical tools, together with decomposition tools and their applicationsSymbolic and numerical equipment for fixing linear PDEs with Maple, Mathematica, and MATLAB®Many new difficulties, illustrative examples, tables, and figuresTo accommodate diversified mathematical backgrounds, the authors steer clear of anyplace attainable using particular terminology, define the various equipment in a schematic, simplified demeanour, and set up the cloth in expanding order of complexity.

Stability Analysis of Impulsive Functional Differential Equations (De Gruyter Expositions in Mathematics)

This ebook is dedicated to impulsive sensible differential equations that are a usual generalization of impulsive traditional differential equations (without hold up) and of practical differential equations (without impulses). this day the qualitative conception of such equationsis less than quick improvement.

Additional resources for Basic Theory of Fractional Differential Equations

Sample text

Download PDF sample

Rated 4.03 of 5 – based on 9 votes