Advanced Topics In Fractional Differential Equations
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Advanced Topics in Fractional Differential Equations
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers’ understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors
Advances in Fractional Calculus
Author: J. Juan Rosales García
language: en
Publisher: Springer Nature
Release Date: 2025-06-02
This book offers a timely snapshot of research in fractional calculus. Based on peer-reviewed, selected contributions to the 6th Mexican Workshop on Fractional Calculus (MWFC), held on October 9-11, 2024 at the University of Guanajuato, in León, Guanajuato México, it offers extensive information on current trends. Chapters cover advances on fractional derivatives and integrals, and fractional differential equations, together with interdisciplinary applications of fractional calculus to real-world scenarios, chaotic and complex systems, and control.
Advanced Topics On Semilinear Evolution Equations
Author: Mouffak Benchohra
language: en
Publisher: World Scientific
Release Date: 2025-01-07
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fréchet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.