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.


- Pp. i
Francesco Mainardi
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- Pp. II-III (2)
Sachin Bhalekar
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List of Contributors

- Pp. iv-v (2)
Sachin Bhalekar
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Solving Fractional Diffusion Equation by Wavelet Methods

- Pp. 1-32 (32)
Zhijiang Zhang, Weihua Deng
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A Survey on the Recent Results Regarding Maximum Principles for the Time-Fractional Diffusion Equations

- Pp. 33-69 (37)
Yuri Luchko, Masahiro Yamamoto
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Integral-Balance Solution to Nonlinear Subdiffusion Equation

- Pp. 70-105 (36)
Jordan Hristov
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Analysis of Solution and System Identification of Coupled Fractional Delay Differential Equation by Shifted Jacobi Polynomials

- Pp. 106-131 (26)
B. Ganesh Priya, P. Muthukumar, P. Balasubramaniam
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Monotone Iteration Principle in the Theory of Hadamard Fractional Delay Differential Equations

- Pp. 132-158 (27)
Kishor D. Kucche
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Dynamics of Fractional Order Modified Bhalekar- Gejji System

- Pp. 159-182 (24)
Sachin Bhalekar
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Grunwald-Letnikov Derivative: Analysis in Range of First Order

- Pp. 183-198 (16)
Radosław Cioc
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GPU Computing of Special Mathematical Functions used in Fractional Calculus

- Pp. 199-232 (34)
Parag Patil, Navin Singhaniya, Chaitanya Jage, Vishwesh A. Vyawahare, Mukesh D. Patil, P.S.V. Nataraj
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New Iterative Method: A Review

- Pp. 233-268 (36)
Varsha Daftardar-Gejji, Manoj Kumar
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Derivatives with Non-Singular Kernels from the Caputo-Fabrizio Definition and Beyond: Appraising Analysis with Emphasis on Diffusion Models

- Pp. 269-341 (73)
Jordan Hristov
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Fractional Order Nonlinear Systems: Some Open Problems in Numerical Computations and Chaos Theory

- Pp. 342-347 (6)
Sachin Bhalekar
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Subject Index

- Pp. 348-359 (12)
Sachin Bhalekar
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.Fundamentals of Mathematics in Medical Research: Theory and Cases.
.Advanced Mathematical Applications in Data Science.
.Markov Chain Process (Theory and Cases).
.Advances in Special Functions of Fractional Calculus: Special Functions in Fractional Calculus and Their Applications in Engineering.