Scalar Singularly Perturbed Cauchy Problem for a Differential Equation of Fractional Order
DOI:
https://doi.org/10.24203/ajfam.v7i1.5619Keywords:
- singular perturbation, asymptotic solution, regularization of the problem, iterative problem, computer mathematics system MapleAbstract
In this paper we consider initial problem for an ordinary differential equation of fractional order with a small parameter for the derivative. S.A. Lomov regularization method is used to construct an asymptotic approximate solution of the problem with accuracy up to any power of a small parameter. Using the computer mathematics system (CMS) Maple, a symbolic solution of the original problem is obtained, and solution schedules are constructed, depending on the initial data and various values of the small parameter. It is shown that the asymptotic solution presented in the form of a specific convergent series and the solution represented by the CMS Maple coincides with the exact solution of the original problem.
Â
References
Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M. (2014) A new definition of fractional derivative, Journal Comput. Appl. Math., 264, 65–70.
Katugampola, U. (2015) Correction to “What is a fractional derivative?†by Ortigueira and Machado. Journal Computational Physics, 293, 4–13.
Lomov, S.A. (1992) Introduction to General Theory of Singular Perturbations, 112, American Mathematical Society, Providence, USA.
Kirsanov, M.N. (2007) Counts of in Maple, M, Fizmatlit.
Downloads
Published
Issue
Section
License
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.
