Bøger af Bernard Gibson

Fractional calculus is a branch of mathematical analysis that studies the different possibilities of defining real number powers or complex number powers of the differentiation operator and the integration operator. It also focuses on developing a calculus for such operators generalizing the classical one. Fractional differential equations are a generalization of differential equations through the application of fractional calculus. They are also referred to as extraordinary differential equations. They are widely used in various disciplines such as mathematics, physics, chemistry, biology, medicine, mechanics, control theory, signal and image processing, and environmental science. Most of the computational tools do not have in-built functions for solving fractional differential equations or differential equations having non-integer order. However, there are certain numerical methods for solving fractional-order problems such as certain MATLAB routines. This book provides a broad overview of the numerical methods used for solving fractional differential equations. It will serve as a valuable source of reference for students and mathematics researchers.

Fractional differential equations or fractional order differential equations are generalized and non-integer order differential equations, which can be obtained in time and space with a power law memory kernel of the non-local relationships. They are also known as extraordinary differential equations. They are used to describe the functioning of various complex and non-local systems with memory. Fractional differential equations are applied extensively in various fields including medicine, mechanics, control theory, signal and image processing, environmental science, mathematics, physics, chemistry, and biology. Some of its prominent applications include time-space fractional diffusion equation models, acoustic wave equations for complex media and electrochemical analysis. This book covers the latest researches on the theory and applications of fractional differential equations. It strives to provide a fair idea about these equations and to help develop a better understanding of the latest advances in their study. The book is an invaluable asset for researchers working in the areas of pure mathematics, applied mathematics, statistics, and engineering.