Editor: Sachin Bhalekar

Series Title: Current Developments in Mathematical Sciences

Frontiers in Fractional Calculus

Volume 1

eBook: US $49 Special Offer (PDF + Printed Copy): US $147
Printed Copy: US $123
Library License: US $196
ISSN: 2589-2711 (Print)
ISSN: 2589-272X (Online)
ISBN: 978-1-68108-600-2 (Print)
ISBN: 978-1-68108-599-9 (Online)
Year of Publication: 2018
DOI: 10.2174/97816810859991180101


This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts:

  1. - Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations.
  2. - Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives.
  3. - Computational Techniques: GPU computing of special mathematical functions used in fractional calculus.
  4. - Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system

This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.


Fractional calculus, in allowing integrals and derivatives of any positive order (the term fractional is kept only for historical reasons), can be considered a branch of mathematical physics that deals with integro-differential equations, where integrals are of convolution type and exhibit mainly singular kernels of power law or logarithm type.

It is a subject that has gained considerably popularity and importance in the past few decades in diverse fields of science and engineering.

The purpose of this book is to establish a collection of articles that reflect some mathematical and conceptual developments in the field of fractional calculus and explore the scope for applications in applied sciences. The book is divided in 4 sections as follows where the authors are outlined.

I congratulate with the Editor, PhD Sachin Bhalekar who was able to collect so a variety of topics of which the reader can evaluate the relevance.

Francesco Mainardi
Professor of Mathematical Physics
University of Bologna