Study of the Existence and Uniqueness of Global Solution for the Fractional Second Order Nonlinear Integro –Differential Equations with Boundary Conditions
DOI:
https://doi.org/10.31642/JoKMC/2018/050201Keywords:
Differential Equations, Fractional Second Order Nonlinear Integro –Differential EquationsAbstract
In this paper, the existence of the global solution and its uniqueness is studied for the Second Order Nonlinear Integro–Differential Fractional Equations with boundary conditions by utilizing the Picard approximation method which is given by Sturble, 1962. Furthermore, several given results by Butris, 2010 have been extendedDownloads
References
R. N. Butris and H. Abdol–Qadir, “Some results in theoryintegro–differential equation of fractional order,” Jouranl Educ. Sci., vol. 49, pp. 88–98, 2001.
I. Ali, V. Kiryakova, and S. L. Kalla, “Solutions of fractional multi-order integral and differential equations using a Poisson-type transform,” J. Math. Anal. Appl., vol. 269, no. 1, pp. 172–199, May 2002. DOI: https://doi.org/10.1016/S0022-247X(02)00012-4
H. A. H. Salem and Ahmed M. A. El-Sayed, “Weak solution for fractional order integral equations in reflexive Banach spaces,” Math. Slovaca, vol. 55, no. 2, pp. 169– 181, 2005.
M. H. T. Alshbool, A. S. Bataineh, I. Hashim, and O. R. Isik, “Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions,” J. King Saud Univ. - Sci., vol. 29, no. 1, pp. 1–18, 2017. DOI: https://doi.org/10.1016/j.jksus.2015.11.004
R. N. Butris, “Existence , Uniqueness and Stability Solution of Non-linear System of Integro Differential Equation of Volterra type,” vol. 2, no. 7, pp. 140–158, 2015.
G. S. Jameel, “Existence and Uniqueness Solution of Fractional Nonlinear Integro –Differential Equation of order (2α) with Boundary Conditions,” Tikrit J. Pure Sci., vol. 18, no. 3, pp. 211–223, 2013.
L. Byszewski, “Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem,” J. Math. Anal. Appl., vol. 162, no. 2, pp. 494–505, Dec. 1991. DOI: https://doi.org/10.1016/0022-247X(91)90164-U
J. H. Barrett, “Differential equations of non–Integro Order,” Can. J. Math., vol. 6, 1954. DOI: https://doi.org/10.4153/CJM-1954-058-2
R. N. Butris and D. S. Abdullah, “Solution of Integro-differential Equation of the first order with the operators,” no. 6, pp. 122–133, 2015.
N. Kosmatov, “Integral equations and initial value problems for nonlinear differential equations of fractional order,” Nonlinear Anal. Theory, Methods Appl., vol. 70, no. 7, pp. 2521–2529, 2009. DOI: https://doi.org/10.1016/j.na.2008.03.037
Z. Wei, Q. Li, and J. Che, “Initial value problems for fractional differential equations involving Riemann–Liouville sequential fractional derivative,” J. Math. Anal. Appl., vol. 367, no. 1, pp. 260–272, 2010. DOI: https://doi.org/10.1016/j.jmaa.2010.01.023
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