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On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-11-22
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
The purpose of this paper is to investigate the existence of solutions to the following initial value problem for nonlinear fractional differential equation involving Caputo sequential fractional derivative Dc0α2Dc0α1yxp-2Dc0α1yx=fx,yx, x>0, y(0)=b0, Dc0α1y(0)=b1, where Dc0α1, Dc0α2 are Caputo fractional derivatives, 0<α1, α2≤1, p>1, and b0,b1∈R.
Local existence of solutions is established by employing Schauder fixed point theorem.
Then a growth condition imposed to f guarantees not only the global existence of solutions on the interval [0,+∞), but also the fact that the intervals of existence of solutions with any fixed initial value can be extended to [0,+∞).
Three illustrative examples are also presented.
Existence results for initial value problems of ordinary differential equations with p-Laplacian on the half-axis follow as a special case of our results.
American Psychological Association (APA)
Ye, Hailong& Huang, Rui. 2015. On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative. Advances in Mathematical Physics،Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1052883
Modern Language Association (MLA)
Ye, Hailong& Huang, Rui. On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative. Advances in Mathematical Physics No. 2015 (2015), pp.1-9.
https://search.emarefa.net/detail/BIM-1052883
American Medical Association (AMA)
Ye, Hailong& Huang, Rui. On the Nonlinear Fractional Differential Equations with Caputo Sequential Fractional Derivative. Advances in Mathematical Physics. 2015. Vol. 2015, no. 2015, pp.1-9.
https://search.emarefa.net/detail/BIM-1052883
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1052883