Svetlin Georgiev, PhD – Sorbonne University, Paris, France

Series: Mathematics Research Developments; Theoretical and Applied Mathematics
BISAC: MAT007000; MAT003000; MAT037000
DOI: https://doi.org/10.52305/RWMH0412

This book is devoted to recent investigations in different areas of differential equations. The book contains nine chapters. In Chapter 1, a class of one-dimensional coupled nonlinear Burgers equations are investigated for existence and nonuniqueness of classical solutions. Chapter 2 presents foundational concepts essential to the study of linear difference equations and their solution structures. In Chapter 3, the Avery-Henderson twin fixed point theorem for sums of operators is extended. Chapter 4 is devoted to the pantograph equation that is a class of functional differential equations characterized by the presence of a delayed argument scaled by a constant factor. Chapter 5 concerns the study of the controllability for some partial functional stochastic integro-differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The main objective of Chapter 6 is to establish a new set of sufficient conditions for the approximate controllability of evolution stochastic functional differential equations driven by a fractional Brownian motion in Hilbert space. Chapter 7 aims to propose a predictive model for financial historical data using a linear dynamic model. Chapter 8 concerns first-order differential equations that are fundamental to introductory differential equations courses, providing essential building blocks for understanding the entire subject. Finally, Chapter 9 is devoted to the solvability of the heat equation in time-dependent domains.

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