Presence and diversity of positive solutions for a Caputotype fractional order nonlinear differential equation with an advanced argument
Volume 23, Issue 3, pp 230244
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 Caputotype fractionalorder nonlinear differential equation (CFONLDE for short) with an advanced argument under threepoint boundary value conditions (BVCs for short). GuoKrasnoselskii's fixed point theorem and Fixedpoint 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.
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ISRP Style
Md. Asaduzzaman, Adem Kilicman, Md. Zulfikar Ali, Presence and diversity of positive solutions for a Caputotype fractional order nonlinear differential equation with an advanced argument, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 230244
AMA Style
Asaduzzaman Md., Kilicman Adem, Ali Md. Zulfikar, Presence and diversity of positive solutions for a Caputotype fractional order nonlinear differential equation with an advanced argument. J Math Comput SCIJM. (2021); 23(3):230244
Chicago/Turabian Style
Asaduzzaman, Md., Kilicman, Adem, Ali, Md. Zulfikar. "Presence and diversity of positive solutions for a Caputotype fractional order nonlinear differential equation with an advanced argument." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 230244
Keywords
 CFONLDE with an advanced argument
 threepoint boundary value conditions
 GuoKrasnoselskii fixed point theorem
 fixedpoint index theory
 positive solution
MSC
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