Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis

Vidhya Saraswathy Krishnasamy; Somayeh Mashayekhi; Mohsen Razzaghi

Volume 4 Issue 1

Jan. 2017

IEEE/CAA Journal of Automatica Sinica

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Vidhya Saraswathy Krishnasamy, Somayeh Mashayekhi and Mohsen Razzaghi, "Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 98-106, Jan. 2017.

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Vidhya Saraswathy Krishnasamy, Somayeh Mashayekhi and Mohsen Razzaghi, "Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis," IEEE/CAA J. Autom. Sinica, vol. 4, no. 1, pp. 98-106, Jan. 2017.

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Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis

1.
Department of Mathematics and Statistics, Mississippi State University, MS 39762, USA
2.
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA

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Author Bio:
Vidhya Saraswathy Krishnasamy received her undergraduate and master's degree in mathematics from Sri G.V.G. Vishalakshi College for Women, Udumalpet, India. She graduated from Mississippi State University (MSU), USA with her Ph.D. degree in August, 2016. She has diverse research interests, which include fractional calculus, orthogonal functions and its applications to dynamical systems, graph theory, number theory, cryptography and its applications (e-mail:vk81@msstate.edu)

Somayeh Mashayekhi graduated from Mississippi State University (MSU), USA, in 2015. She received her first Ph.D. degree from Alzahra University in 2013, and her second Ph.D. degree from MSU in 2015. She is, currently, a post doctoral research associate in computational science and engineering, Department of Mathematics, Florida State University. Her research interests include optimal control, delay system, fractional calculus, orthogonal functions and its applications to dynamical systems (e-mail: sm2395@msstate.edu)
Corresponding author: Mohsen Razzaghi received his undergraduate degree in mathematics from the University of Sussex in England. He went to Canada and received his master's degree in applied mathematics from the University ofWaterloo. He returned to the University of Sussex and obtained his Ph.D.. After that, he has taught and served in several administrative positions in Iran and in the USA. Since 1986, he has been at the Department of Mathematics and Statistics at Mississippi State University, where he is currently a professor and the department head. During the academic years 2011-2012 and 2015-2016, he was a Fulbright Scholar at the Department of Mathematics and Computer Science at the Technical University of Civil Engineering in Bucharest, Romania. His area of research centers on optimal control, orthogonal functions and wavelets in dynamical system, and fractional calculus. He has over 150 refereed journal publications in mathematics, mathematical physics, and engineering. (e-mail:razzaghi@math.msstate.edu)
Received Date: 2015-08-08
Accepted Date: 2016-04-18

Abstract

Abstract

In this paper, a new numerical method for solving fractional differential equations (FDEs) is presented. The method is based upon the fractional Taylor basis approximations. The operational matrix of the fractional integration for the fractional Taylor basis is introduced. This matrix is then utilized to reduce the solution of the fractional differential equations to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of this technique.
- Caputo derivative,
- fractional differential equations (FEDs),
- fractional Taylor basis,
- operational matrix,
- Riemann-Liouville fractional integral operator

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Numerical Solutions of Fractional Differential Equations by Using Fractional Taylor Basis

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