Affiliation:
1. Department of Mathematics , University of Peshawar , Peshawar 25000 , Pakistan
Abstract
Abstract
In this typescript, we study system of nonlinear implicit coupled differential equations of arbitrary (non–integer) order having nonlocal boundary conditions on closed interval [0, 1] with Caputo fractional derivative. We establish sufficient conditions for the existence, at least one and a unique solution of the proposed coupled system with the help of Krasnoselskii’s fixed point theorem and Banach contraction principle. Moreover, we scrutinize the Hyers–Ulam stability for the considered problem. We present examples to illustrate our main results.
Subject
Applied Mathematics,General Physics and Astronomy,Mechanics of Materials,Engineering (miscellaneous),Modeling and Simulation,Computational Mechanics,Statistical and Nonlinear Physics
Reference30 articles.
1. J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Advances in Fractional Calculus, Dordrecht, Springer, 2007.
2. K. B. Oldham, “Fractional differential equations in electrochemistry,” Adv. Eng. Software, vol. 41, pp. 9–12, 2010. https://doi.org/10.1016/j.advengsoft.2008.12.012.
3. B. M. Vintagre, I. Podlybni, A. Hernandez, and V. Feliu, “Some approximations of fractional order operators used in control theory and applications,” Fract. Cal. Appl. Anal., vol. 3, no. 3, pp. 231–248, 2000.
4. V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Beijing, Springer, Heidelberg, Higher Education Press, 2010.
5. F. A. Rihan, “Numerical modeling of fractional order biological systems,” Abstr. Appl. Anal., vol. 2013, pp. 1–11, 2013. https://doi.org/10.1155/2013/816803.
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