There has been a great advancement in the study of fractional-order nonlocal nonlinear boundary value problems during the last few decades. The interest in the subject of fractional-order boundary value problems owes to the extensive application of fractional differential equations in many engineering and scientific disciplines. Fractional-order differential and integral operators provide an excellent instrument for the description of memory and hereditary properties of various materials and processes, which contributed significantly to the popularity of the subject and motivated many researchers and modelers to shift their focus from classical models to fractional order models. Some peculiarities of physical, chemical or other processes happening inside the domain cannot be formulated with the aid of classical boundary conditions. This limitation led to the consideration of nonlocal and integral conditions which relate the boundary values of the unknown function to its values at some interior positions of the domain.The main objective for writing this book is to present some recent results on single-valued and multi-valued boundary value problems, involving different kinds of fractional differential and integral operators, and several kinds of nonlocal multi-point, integral, integro-differential boundary conditions. Much of the content of this book contains the recent research published by the authors on the topic.
Contents:
- Preliminaries
- Nonlocal Boundary Value Problems with Different Kinds of Boundary Conditions
- Nonlocal Fractional Boundary Value Problems with Integral Boundary Conditions
- Nonlinear Fractional-Order Boundary Value Problems with Boundary Conditions Involving Fractional Derivative Operators
- Nonlocal Fractional-Order Boundary Value Problems with Discrete and Integral Boundary Conditions
- Positive Solutions for Nonlocal Fractional-Order Boundary Value Problems
- Nonlocal Boundary Value Problems with Generalized Fractional Integral and Derivative
Readership: Researchers working in the field of fractional calculus/boundary value problems; graduate students with major in fractional order boundary value problems; researchers working on the theoretical aspects of fractional differential equations and inclusions.
Key Features:
- This book provides an up-to-date development on the topic of nonlocal nonlinear boundary value problems dealing with fractional differential equations and inclusions
- The existence and uniqueness results for a variety of nonlocal nonlinear boundary value problems, based on different tools of the fixed-point theory and monotone iterative technique, are presented
- The material chosen for this book is significant in the sense that it covers different kinds of nonlocal fractional-order boundary value problem, which are studied with the aid of a variety of tools of modern functional analysis
- This book distinguishes itself from the available ones
