A new operational approach for solving fractional calculus and frational differential equations numerically

Jiunn Lin Wu, Chin-Hsing Chen

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Fractional calculus is the generalization of the operators of differential and integration to non-integer order, and a differential equation involving the fractional calculus operators such as d1/2/dt1/2 and d-1/2/dt-1/2 is called the fractional differential equation. They have many applications in science and engineering. But not only its analytical solutions exist only for a limited number of cases, but also, the numerical methods are difficult to solve. In this paper we propose a new numerical method based on the operational matrices of the orthogonal functions for solving the fractional calculus and fractional differential equations. Two classical fractional differential equation examples are included for demonstration. They show that the new approach is simper and more feasible than conventional methods. Advantages of the proposed method include (1) the computation is simple and computer oriented; (2) the scope of application is wide; and (3) the numerically unstable problem never occurs in our method.

Original languageEnglish
Pages (from-to)1077-1082
Number of pages6
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE87-A
Issue number5
Publication statusPublished - 2004 Jan 1

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Fractional Calculus
Fractional Differential Equation
Differential equations
Differential equation
Numerical Methods
Mathematical operators
Operational Matrix
Numerical methods
Orthogonal Functions
Operator
Orthogonal functions
Analytical Solution
Unstable
Engineering
Demonstrations

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

Cite this

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