Single and dual solutions of fractional order differential equations based on controlled Picard’s method with Simpson rule
Joint Authors
Semary, Murad S.
Radwan, Ahmad G.
Hasan, Hani N.
Source
Arab Journal of Basic and Applied Sciences
Issue
Vol. 24, Issue 0 (31 Oct. 2017), pp.247-253, 7 p.
Publisher
University of Bahrain College of Science
Publication Date
2017-10-31
Country of Publication
Bahrain
No. of Pages
7
Main Subjects
Natural & Life Sciences (Multidisciplinary)
Abstract EN
This paper presents a semi-analytical method for solving fractional differential equations with strong terms like (exp, sin, cos,.
.
.).
An auxiliary parameter is introduced into the well-known Picard’s method and so called controlled Picard’s method.
The proposed approach is based on a combination of controlled Picard’s method with Simpson rule.
This approach can cover a wider range of integer and fractional orders differential equations due to the extra auxiliary parameter which enhances the convergence and is suitable for higher order differential equations.
The proposed approach can be effectively applied to Bratu’s problem in fractional order domain to predict and calculate all branches of problem solutions simultaneously.
Also, it is tested on other fractional differential equations like nonlinear fractional order Sine-Gordon equation.
The results demonstrate reliability, simplicity and efficiency of the approach developed.
American Psychological Association (APA)
Semary, Murad S.& Hasan, Hani N.& Radwan, Ahmad G.. 2017. Single and dual solutions of fractional order differential equations based on controlled Picard’s method with Simpson rule. Arab Journal of Basic and Applied Sciences،Vol. 24, no. 0, pp.247-253.
https://search.emarefa.net/detail/BIM-760790
Modern Language Association (MLA)
Semary, Murad S.…[et al.]. Single and dual solutions of fractional order differential equations based on controlled Picard’s method with Simpson rule. Arab Journal of Basic and Applied Sciences Vol. 24 (Oct. 2017), pp.247-253.
https://search.emarefa.net/detail/BIM-760790
American Medical Association (AMA)
Semary, Murad S.& Hasan, Hani N.& Radwan, Ahmad G.. Single and dual solutions of fractional order differential equations based on controlled Picard’s method with Simpson rule. Arab Journal of Basic and Applied Sciences. 2017. Vol. 24, no. 0, pp.247-253.
https://search.emarefa.net/detail/BIM-760790
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 253
Record ID
BIM-760790