Fractional calculus falls under the domain of mathematical analysis. It focuses on the study of the differentiation operator in terms of real and complex number powers. Fractional calculus has various applications across other scientific fields such as polymer chemistry through structural damping models, in quantum theory through the analysis of Schrödinger's equation, etc. This book elucidates new techniques and their applications in a multidisciplinary manner. The chapters provide significant information of this field to help develop a good understanding of fractional calculus and related fields. It also attempts to understand the multiple branches that fall under this discipline and how such concepts have practical applications. It aims to serve as a resource guide for students and experts alike as well as contribute to the growth of the discipline.