This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.

This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering.

The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green''s function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented.

With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well.

This textbook provides a comprehensive exploration of special functions and fractional calculus, offering a structured approach through solved and proposed exercises. Covering key mathematical concepts such as Mittag-Leffler functions, Kilbas-Saigo functions, and the Erdélyi-Kober fractional integral, it balances theoretical insights with practical applications. Appendices introduce Barnes G-functions and demonstrate the use of Mathematica for fractional calculus, expanding the book’s accessibility. With an updated index and extensive references, this edition serves as a valuable resource for researchers, graduate students, and professionals in applied mathematics and related fields.

This book is an exposition of the algebra and calculus of differentialforms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to aformulation of important concepts of differential geometry indispensable for anin-depth understanding of space-time physics.The formalism discloses the hidden geometrical nature of spinor fields.Maxwell, Dirac and Einstein fields are shown to have representatives by objectsof the same mathematical nature, namely sections of an appropriate Cliffordbundle. This approach reveals unity in diversity and suggests relationshipsthat are hidden in the standard formalisms and opens new paths for research.This thoroughly revised second edition also adds three new chapters: on the Cliffordbundle approach to the Riemannian or semi-Riemannian differential geometry ofbranes; on Komar currents in the context of the General Relativity theory; andan analysis of the similarities and main differences between Dirac, Majoranaand ELKO spinor fields.The exercises with solutions, thecomprehensive list of mathematical symbols, and the list of acronyms andabbreviations are provided for self-study for students as well as for classes.

From the reviews of the firstedition:

“The text is written in a veryreadable manner and is complemented with plenty of worked-out exercises whichare in the style of extended examples. ... their book could also serve as atextbook for graduate students in physics or mathematics." (AlbertoMolgado, Mathematical Reviews, 2008 k)

This book contains a brief historical introduction and state of the art in fractional calculus. The author introduces some of the so-called special functions, in particular, those which will be directly involved in calculations. The concepts of fractional integral and fractional derivative are also presented. Each chapter, except for the first one, contains a list of exercises containing suggestions for solving them and at last the resolution itself. At the end of those chapters there is a list of complementary exercises. The last chapter presents several applications of fractional calculus.

This book compiles an extensive list of solved and proposed problems in mathematical topics in analysis, aimed at students of mathematics, applied mathematics, physics, and engineering.

The book begins with an exploration of simple linear and nonlinear ordinary differential equations in Chapter 1, advancing through topics such as power series and the Frobenius method for solving differential equations in Chapter 2. In subsequent chapters, the discussion expands to include functions of complex variables, special functions constructed through the hypergeometric function, and series solutions including Fourier, Fourier-Bessel, and Fourier-Legendre series. Problems in integral transforms, Sturm-Liouville systems, Green''s function, linear partial differential equations are also included. The work finishes with a special chapter on fractional calculus and practical applications of the topics presented.

With solved examples and step-by-step exercises, this book can be of value to undergraduate and graduate students seeking a hands-on approach on the listed topics, and as a bibliographical complement to STEM courses as well.

This textbook provides a comprehensive exploration of special functions and fractional calculus, offering a structured approach through solved and proposed exercises. Covering key mathematical concepts such as Mittag-Leffler functions, Kilbas-Saigo functions, and the Erdélyi-Kober fractional integral, it balances theoretical insights with practical applications. Appendices introduce Barnes G-functions and demonstrate the use of Mathematica for fractional calculus, expanding the book’s accessibility. With an updated index and extensive references, this edition serves as a valuable resource for researchers, graduate students, and professionals in applied mathematics and related fields.

This book is an exposition of the algebra and calculus of differentialforms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to aformulation of important concepts of differential geometry indispensable for anin-depth understanding of space-time physics.The formalism discloses the hidden geometrical nature of spinor fields.Maxwell, Dirac and Einstein fields are shown to have representatives by objectsof the same mathematical nature, namely sections of an appropriate Cliffordbundle. This approach reveals unity in diversity and suggests relationshipsthat are hidden in the standard formalisms and opens new paths for research.This thoroughly revised second edition also adds three new chapters: on the Cliffordbundle approach to the Riemannian or semi-Riemannian differential geometry ofbranes; on Komar currents in the context of the General Relativity theory; andan analysis of the similarities and main differences between Dirac, Majoranaand ELKO spinor fields.The exercises with solutions, thecomprehensive list of mathematical symbols, and the list of acronyms andabbreviations are provided for self-study for students as well as for classes.

From the reviews of the firstedition:

“The text is written in a veryreadable manner and is complemented with plenty of worked-out exercises whichare in the style of extended examples. ... their book could also serve as atextbook for graduate students in physics or mathematics." (AlbertoMolgado, Mathematical Reviews, 2008 k)