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

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.


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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


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