Fractional Differential Equations: Numerical Methods for Applications

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.