Frontiers in Fractional Calculus

Current Developments in Mathematical Sciences Vol. 1; Frontiers in Fractional Calculus

Release Date: 01-Dec-2020

Book Highlights ~ Bentham Books

This book is by Sachin Bhalekar is published on March 21st, 2018.

Fractional Calculus is a very popular subject among mathematicians and applied scientists. The nonlocal operators in fractional calculus provide solutions for challenging research topics and problems for mathematicians. On the other hand, applied scientists usually find these operators more useful for their work than classical integer order operators.

Frontiers in Fractional Calculus 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.

Keywords: Algorithms/Models, Calculations/Problem-Solving, Mathematics/Statistics, Number Literacy/General Statistics