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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shuman Meng & Yujun Cui, 2019. "The Extremal Solution To Conformable Fractional Differential Equations Involving Integral Boundary Condition," Mathematics, MDPI, vol. 7(2), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:186-:d:206451
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    References listed on IDEAS

    as
    1. Kosmatov, Nickolai & Jiang, Weihua, 2016. "Resonant functional problems of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 573-579.
    2. Lu, Changna & Fu, Chen & Yang, Hongwei, 2018. "Time-fractional generalized Boussinesq equation for Rossby solitary waves with dissipation effect in stratified fluid and conservation laws as well as exact solutions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 104-116.
    3. Yujun Cui & Yumei Zou, 2014. "Existence Results and the Monotone Iterative Technique for Nonlinear Fractional Differential Systems with Coupled Four-Point Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, July.
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    Cited by:

    1. Gauhar Rahman & Kottakkaran Sooppy Nisar & Thabet Abdeljawad & Samee Ullah, 2020. "Certain Fractional Proportional Integral Inequalities via Convex Functions," Mathematics, MDPI, vol. 8(2), pages 1-11, February.

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