An Accurate Spectral Galerkin Method for Solving Multiterm Fractional Differential Equations
Joint Authors
Bhrawy, Ali H.
Alofi, Abdulaziz
Source
Mathematical Problems in Engineering
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-06-12
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This paper reports a new formula expressing the Caputo fractional derivatives for any order of shifted generalized Jacobi polynomials of any degree in terms of shifted generalized Jacobi polynomials themselves.
A direct solution technique is presented for solving multiterm fractional differential equations (FDEs) subject to nonhomogeneous initial conditions using spectral shifted generalized Jacobi Galerkin method.
The homogeneous initial conditions are satisfied exactly by using a class of shifted generalized Jacobi polynomials as a polynomial basis of the truncated expansion for the approximate solution.
The approximation of the spatial Caputo fractional order derivatives is expanded in terms of a class of shifted generalized Jacobi polynomials Jnα,−β(x) with x∈(0,1), and n is the polynomial degree.
Several numerical examples with comparisons with the exact solutions are given to confirm the reliability of the proposed method for multiterm FDEs.
American Psychological Association (APA)
Bhrawy, Ali H.& Alofi, Abdulaziz. 2014. An Accurate Spectral Galerkin Method for Solving Multiterm Fractional Differential Equations. Mathematical Problems in Engineering،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-493958
Modern Language Association (MLA)
Bhrawy, Ali H.& Alofi, Abdulaziz. An Accurate Spectral Galerkin Method for Solving Multiterm Fractional Differential Equations. Mathematical Problems in Engineering No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-493958
American Medical Association (AMA)
Bhrawy, Ali H.& Alofi, Abdulaziz. An Accurate Spectral Galerkin Method for Solving Multiterm Fractional Differential Equations. Mathematical Problems in Engineering. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-493958
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-493958