On the Question of Asymptotic Integration of Singularly Perturbed Fractional-Order Problems
Keywords:matrix-function, vector-function, differential equation of fractional order, regularization, asymptotic, iterative problems, normal and unique solvability.
In this paper we consider an initial problem for systems of differential equations of fractional order with a small parameter for the derivative. Regularization problem is produced, and algorithm for normal and unique solubility of general iterative systems of differential equations with partial derivatives is given.
Kalimbetov, B.T. and Safonov, V.F. (1995) A regularization method for systems with unstable spectral value of the kernel of the integral operator. Journal Differential equations, 31, 647-656.
Kalimbetov, B.T., Temirbekov, M.A. and Khabibullayev, Zh.O. (2012) Asymptotic solutions of singular perturbed problems with an instable spectrum of the limiting operator. Journal Abstract and Applied Analysis, 120192.
Katugampola, U. (2015) Correction to â€œWhat is a fractional derivative?â€ by Ortigueira and Machado. Journal Computational Physics, 293, 4â€“13.
R. Khalil, R., Al Horani, M., Yousef, A. and Sababheh, M. A new definition of fractional derivative. Journal Comput. Appl. Math., 264, 65â€“70.
Khalil, R., Anderson, D. and Al Horani, M. (2014) Undetermined coefficients for local fractional differential equations. URL: https://www.researchgate.net/publication/303903312.
Lomov, S.A. Introduction to General Theory of Singular Perturbations, 112, American Mathematical Society, Providence, USA. (1992)
How to Cite
- 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.