Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument
Volume 23, Issue 3, pp 230--244
http://dx.doi.org/10.22436/jmcs.023.03.06
Publication Date: November 11, 2020
Submission Date: July 10, 2020
Revision Date: September 07, 2020
Accteptance Date: October 09, 2020
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Authors
Md. Asaduzzaman
- Department of Mathematics, Islamic University, Kushtia, Bangladesh.
Adem Kilicman
- Department of Mathematics, Universiti Putra Malaysia, Selangor, Malaysia.
Md. Zulfikar Ali
- Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh.
Abstract
This article aims to construct the presence and diversity principles of minimum one or two positive solutions for a Caputo-type fractional-order nonlinear differential equation (CFONLDE for short) with an advanced argument under three-point boundary value conditions (BVCs for short). Guo-Krasnoselskii's fixed point theorem and Fixed-point index theory in cone spaces are used to analyze this article. First, the Green's function of the corresponding boundary value problem for a linear fractional differential equation with an advanced argument has been established. Next, several essential properties of that Green's function have been proved. Finally, in cone spaces, some novel presence and diversity principles of minimum of one or two positive solutions for a CFONLDE with an advanced argument are obtained. To support the analytic proof, some particular examples are included.
Share and Cite
ISRP Style
Md. Asaduzzaman, Adem Kilicman, Md. Zulfikar Ali, Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 230--244
AMA Style
Asaduzzaman Md., Kilicman Adem, Ali Md. Zulfikar, Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument. J Math Comput SCI-JM. (2021); 23(3):230--244
Chicago/Turabian Style
Asaduzzaman, Md., Kilicman, Adem, Ali, Md. Zulfikar. "Presence and diversity of positive solutions for a Caputo-type fractional order nonlinear differential equation with an advanced argument." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 230--244
Keywords
- CFONLDE with an advanced argument
- three-point boundary value conditions
- Guo-Krasnoselskii fixed point theorem
- fixed-point index theory
- positive solution
MSC
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