Some basic principles of fractional calculus

In this book, we present an introduction to fractional calculus, including classical definitions of fractional derivatives and integrals such as Grünwald--Letnikov, Riemann--Liouville, and Caputo. We study linear and nonlinear fractional differential equations, focusing on existence and uniqueness results using Laplace transform and fixed point methods. We also introduce the conformable fractional derivative and discuss its applications, including analytical tools such as the fractional Wronskian and Abel-type formulas. This book provides a concise foundation for the study of fractional calculus and its applications.