The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition

Shuman Meng and Yujun Cui
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Shuman Meng: Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266590, China
Yujun Cui: State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China

Mathematics, 2019, vol. 7, issue 2, 1-9

Abstract: In this article, by using the monotone iterative technique coupled with the method of upper and lower solution, we obtain the existence of extremal iteration solutions to conformable fractional differential equations involving Riemann-Stieltjes integral boundary conditions. At the same time, the comparison principle of solving such problems is investigated. Finally, an example is given to illustrate our main results. It should be noted that the conformal fractional derivative is essentially a modified version of the first-order derivative. Our results show that such known results can be translated and stated in the setting of the so-called conformal fractional derivative.

Keywords: fractional differential equations; Riemann-stieltjes integral; monotone iterative method; upper and lower solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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