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Mathematics 2019, 7(2), 186; https://doi.org/10.3390/math7020186

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

1
Department of Applied Mathematics, Shandong University of Science and Technology, Qingdao 266590, China
2
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
*
Author to whom correspondence should be addressed.
Received: 19 January 2019 / Revised: 10 February 2019 / Accepted: 14 February 2019 / Published: 16 February 2019
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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. View Full-Text
Keywords: fractional differential equations; Riemann-stieltjes integral; monotone iterative method; upper and lower solutions fractional differential equations; Riemann-stieltjes integral; monotone iterative method; upper and lower solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Meng, S.; Cui, Y. The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition. Mathematics 2019, 7, 186.

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