On the Parametrization of Nonlinear Impulsive Fractional Integro–Differential System With Non-Separated Integral Coupled Boundary Conditions
DOI:
https://doi.org/10.25271/sjuoz.2020.8.4.768Keywords:
Caputo fractional derivative, fractional integro-differential, integral coupled boundary conditions, Periodic solutions, successive approximation methodAbstract
We give a new investigation of periodic solutions of nonlinear impulsive fractional integro-differential system with different orders of fractional derivatives with non-separated integral coupled boundary conditions. Uniformly Converging of the sequence of functions according to the main idea of the Numerical-analytic technique, from creating a sequence of functions. An example of impulsive fractional system is also presented to illustrate the theory.
References
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Marynets, K. (2016). On construction of the approximate solution of the special type integral boundary-value problem. Electron. J. Qual. Theory Differ. Equ., 6, 1–14.
Mitropolsky Yu. A. & Martynyuk D. I. (1979). For Periodic Solutions for the Oscillations Systems with Retarded Argument, Kiev, Ukraine.
Ronto, M. & Samoilenko, A.M. (2000). Numerical-Analytic Methods in the Theory of Boundary-Value Problems. World Scientific: Singapore.
Ronto, M., Marynets, K.V. & Varha, J.V. (2015). Further results on the investigation of solutions of integral boundary value problems. Tatra Mt. Math. Publ., 63, 247–267.
Sabatier J., Agrawal OP. & Machado, JAT (2007): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht.
Samoilenko A. M. & Ronto N. I. (1976). A Numerical – Analytic Methods for Investigations of Periodic Solutions, Kiev, Ukraine.
Su X. (2009). Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett., 22, 64-69.
Wang J., Xiang H. & Liu Z. (2010). Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations. Int. J. Differ. Equ., Article ID 186928.
Wang, G, Ahmad, B, Zhang, L. & Nieto, JJ. (2014). Comments on the concept of existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 19, 401-403.
Wang, JR, Li, X & Wei, W. (2012). On the natural solution of an impulsive fractional differential equation of order q ∈ (1, 2). Commun. Nonlinear Sci. Numer. Simul. 17, 4384-4.
Zhou, WX & Chu, YD. (2012). Existence of solutions for fractional differential equations with multi-point boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 17, 1142-1148.
Ahmad B. & Nieto J. J. (2014). A class of differential equations of fractional order with multi-point boundary conditions. Georgian Math. J., 21, 243–248.
Bai, ZB & Zhang, S. (2016). Monotone iterative method for a class of fractional differential equations. Electron. J. Differ. Equ. 2016, 06.
Bai, ZB, Dong, XY & Yin, C. (2016). Existence results for impulsive nonlinear fractional differential equation with mixed boundary conditions. Bound. Value Probl. 2016, 63.
Butris R. N. & Taher R. F. (2019). Periodic solution of integro-differential equations depended on special functions with singular kernels and boundary integral conditions. International Journal of Advanced Trends in Computer Science and Engineering. Vol. 8, No.4.
Butris R. N., Rafeeq A. Sh. & Faris, H. S. (2017) Existence, uniqueness and stability of periodic solution for nonlinear system of integro-differential equations”. science Journal of University of Zakho Vol. 5.No. 1 pp. 120-127.
Dong, XY, Bai, ZB & Zhang, SQ. (2017) . Positive solutions to boundary value problems of p-Laplacian with fractional derivative. Bound. Value Probl. 2017, 5.
Farkas M. (1994) Periodic motions ,Springer-Verlag, New York,
Feckan M. & Marynets K. (2018). Approximation approach to periodic BVP for mixed fractional differential systems. J. Comput. Appl. Math., 339, 208–217.
Feckan M. & Marynets K. (2017). Approximation approach to periodic BVP for fractional differential systems. Eur. Phys. J., 226, 3681–3692.
Feckan, M, Zhou, Y. & Wang, JR. (2012). On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 17, 3050-3060.
Henderson J., Luca R. & Tudorache, A. (2015). On a system of fractional equations with coupled integral boundary conditions. Fract. Calc. Appl. Anal., 18, 361–386.
Kilbas A. A., Srivastava H. M & Trujillo J. J. (2006) Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, vol. 204. Elsevier, Amsterdam.
Lakshmikantham V., Leela S. & Devi V. (2009). Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge.
Mahmudov N. I., Emin S. & Bawanah S. (2019). On the Parametrization of Caputo-Type Fractional Differential Equations with Two-Point Nonlinear Boundary Conditions,Mathematics,7,707;doi:10.3390/math7080707.
Marynets, K. (2016). On construction of the approximate solution of the special type integral boundary-value problem. Electron. J. Qual. Theory Differ. Equ., 6, 1–14.
Mitropolsky Yu. A. & Martynyuk D. I. (1979). For Periodic Solutions for the Oscillations Systems with Retarded Argument, Kiev, Ukraine.
Ronto, M. & Samoilenko, A.M. (2000). Numerical-Analytic Methods in the Theory of Boundary-Value Problems. World Scientific: Singapore.
Ronto, M., Marynets, K.V. & Varha, J.V. (2015). Further results on the investigation of solutions of integral boundary value problems. Tatra Mt. Math. Publ., 63, 247–267.
Sabatier J., Agrawal OP. & Machado, JAT (2007): Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering. Springer, Dordrecht.
Samoilenko A. M. & Ronto N. I. (1976). A Numerical – Analytic Methods for Investigations of Periodic Solutions, Kiev, Ukraine.
Su X. (2009). Boundary value problem for a coupled system of nonlinear fractional differential equations. Appl. Math. Lett., 22, 64-69.
Wang J., Xiang H. & Liu Z. (2010). Positive solution to nonzero boundary values problem for a coupled system of nonlinear fractional differential equations. Int. J. Differ. Equ., Article ID 186928.
Wang, G, Ahmad, B, Zhang, L. & Nieto, JJ. (2014). Comments on the concept of existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul. 19, 401-403.
Wang, JR, Li, X & Wei, W. (2012). On the natural solution of an impulsive fractional differential equation of order q ∈ (1, 2). Commun. Nonlinear Sci. Numer. Simul. 17, 4384-4.
Zhou, WX & Chu, YD. (2012). Existence of solutions for fractional differential equations with multi-point boundary conditions. Commun. Nonlinear Sci. Numer. Simul. 17, 1142-1148.
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Published
2020-12-30
How to Cite
Rafeeq, A. S. (2020). On the Parametrization of Nonlinear Impulsive Fractional Integro–Differential System With Non-Separated Integral Coupled Boundary Conditions. Science Journal of University of Zakho, 8(4), 160–168. https://doi.org/10.25271/sjuoz.2020.8.4.768
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