Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

Baitiche, Zidane; Derbazi, Choukri; Alzabut, Jehad; Samei, Mohammad Esmael; Kaabar, Mohammed K. A.; Siri, Zailan

doi:10.3390/fractalfract5030081

Open AccessArticle

Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

by

Zidane Baitiche

^1,†,

Choukri Derbazi

^1,†

,

Jehad Alzabut

^2,3,*,†

,

Mohammad Esmael Samei

^4,5,†

,

Mohammed K. A. Kaabar

^6,7,*,†

and

Zailan Siri

^6,*,†

¹

Laboratoire Equations Differntielles, Department of Mathematics, Faculty of Exact Sciences, University Frères Mentouri, Constantine 25000, Algeria

²

Department of Mathematics and General Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia

³

Department of Industrial Engineering, OSTİM Technical University, Ankara 06374, Turkey

⁴

Department of Mathematics, Faculty of Basic Science, Bu-Ali Sina University, Hamedan 65178, Iran

⁵

Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

⁶

Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur 50603, Malaysia

⁷

Department of Mathematics and Statistics, Washington State University, Pullman, WA 99163, USA

^*

Authors to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Fractal Fract. 2021, 5(3), 81; https://doi.org/10.3390/fractalfract5030081

Submission received: 29 May 2021 / Revised: 19 July 2021 / Accepted: 27 July 2021 / Published: 29 July 2021

(This article belongs to the Special Issue Fractional Order Systems: Deterministic and Stochastic Analysis)

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Abstract

The main contribution of this paper is to prove the existence of extremal solutions for a novel class of

ψ

-Caputo fractional differential equation with nonlinear boundary conditions. For this purpose, we utilize the well-known monotone iterative technique together with the method of upper and lower solutions. Finally, we provide an example along with graphical representations to confirm the validity of our main results.

Keywords: ψ-Caputo operator; extremal solutions; monotone iterative style; upper (lower) solutions; boundary conditions

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MDPI and ACS Style

Baitiche, Z.; Derbazi, C.; Alzabut, J.; Samei, M.E.; Kaabar, M.K.A.; Siri, Z. Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions. Fractal Fract. 2021, 5, 81. https://doi.org/10.3390/fractalfract5030081

AMA Style

Baitiche Z, Derbazi C, Alzabut J, Samei ME, Kaabar MKA, Siri Z. Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions. Fractal and Fractional. 2021; 5(3):81. https://doi.org/10.3390/fractalfract5030081

Chicago/Turabian Style

Baitiche, Zidane, Choukri Derbazi, Jehad Alzabut, Mohammad Esmael Samei, Mohammed K. A. Kaabar, and Zailan Siri. 2021. "Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions" Fractal and Fractional 5, no. 3: 81. https://doi.org/10.3390/fractalfract5030081

APA Style

Baitiche, Z., Derbazi, C., Alzabut, J., Samei, M. E., Kaabar, M. K. A., & Siri, Z. (2021). Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions. Fractal and Fractional, 5(3), 81. https://doi.org/10.3390/fractalfract5030081

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Monotone Iterative Method for ψ-Caputo Fractional Differential Equation with Nonlinear Boundary Conditions

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