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Boundary value problems for fractional differential equations and systems / Bashir Ahmad, Johnny Henderson, Rodica Luca.

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"This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many o...

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Bibliographic Details
Online Access: Full Text (via ProQuest)
Main Authors: Ahmad, Bashir (Mathematics professor) (Author), Henderson, Johnny (Author), Luca, Rodica (Author)
Format: eBook
Language:English
Published: Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., [2021]
Series:Trends in abstract and applied analysis ; v. 9.
Subjects:
Boundary value problems.
Functional differential equations.
Table of Contents:
  • Intro
  • Contents
  • Preface
  • Notations
  • Chapter 1 Preliminaries
  • 1.1 Fractional Integral and Fractional Derivatives
  • 1.2 Fixed Point Theorems
  • Chapter 2 Riemann-Liouville Fractional Differential Equations with Nonlocal Boundary Conditions
  • 2.1 Singular Fractional Differential Equations with Parameters and Multi-Point Boundary Conditions
  • 2.1.1 Auxiliary results
  • 2.1.2 Existence of positive solutions
  • 2.1.3 Examples
  • 2.2 A Fractional Differential Equation with Integral Terms and Multi-Point Boundary Conditions
  • 2.2.1 Existence of nonnegative solutions
  • 2.2.2 An example.
  • 2.3 Semipositone Singular Fractional Boundary Value Problems with Integral Boundary Conditions
  • 2.3.1 Preliminary results
  • 2.3.2 Existence and multiplicity of positive solutions
  • 2.3.3 An example
  • 2.4 Singular Fractional Differential Equations with General Integral Boundary Conditions
  • 2.4.1 Auxiliary results
  • 2.4.2 Existence of multiple positive solutions
  • 2.4.3 An example
  • 2.5 On a Singular Fractional Boundary Value Problem with Parameters
  • 2.5.1 Existence of positive solutions
  • 2.5.2 Some remarks on a related semipositone problem
  • 2.5.3 Examples.
  • 2.6 A Singular Fractional Differential Equation with Integral Boundary Conditions
  • 2.6.1 Preliminary results
  • 2.6.2 Existence and multiplicity of positive solutions
  • 2.6.3 An example
  • Chapter 3 Systems of Two Riemann-Liouville Fractional Differential Equations with Multi-Point Boundary Conditions
  • 3.1 Systems of Fractional Differential Equations with Uncoupled Multi-Point Boundary Conditions
  • 3.1.1 Auxiliary results
  • 3.1.2 Existence and multiplicity of positive solutions
  • 3.2 Systems of Fractional Differential Equations with Coupled Multi-Point Boundary Conditions.
  • 3.2.1 Preliminary results
  • 3.2.2 Nonsingular nonlinearities
  • 3.2.3 Singular nonlinearities
  • 3.2.4 Examples
  • Chapter 4 Systems of Two Riemann-Liouville Fractional Differential Equations with p-Laplacian Operators, Parameters and Multi-Point Boundary Conditions
  • 4.1 Systems of Fractional Differential Equations with Uncoupled Multi-Point Boundary Conditions
  • 4.1.1 Auxiliary results
  • 4.1.2 Existence of positive solutions
  • 4.1.3 Nonexistence of positive solutions
  • 4.1.4 An example
  • 4.1.5 A relation between two supremum limits.
  • 4.2 Systems of Fractional Differential Equations with Coupled Multi-Point Boundary Conditions
  • 4.2.1 Preliminary results
  • 4.2.2 Existence of positive solutions
  • 4.2.3 Nonexistence of positive solutions
  • 4.2.4 An example
  • Chapter 5 Systems of Three Riemann-Liouville Fractional Differential Equations with Parameters and Multi-Point Boundary Conditions
  • 5.1 Systems of Fractional Differential Equations with Uncoupled Multi-Point Boundary Conditions
  • 5.1.1 Auxiliary results
  • 5.1.2 Existence of positive solutions
  • 5.1.3 Nonexistence of positive solutions
  • 5.1.4 Examples.

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