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Extremal Positive Solutions For The Distributed Order Fractional Hybrid Differential Equations | ||
| Computational Methods for Differential Equations | ||
| مقاله 4، دوره 1، شماره 2، دی 2013، صفحه 120-134 اصل مقاله (187.5 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Hossein Noroozi؛ Alireza Ansari* | ||
| Shahrekord University | ||
| چکیده | ||
| In this article, we prove the existence of extremal positive solution for the distributed order fractional hybrid differential equation $$int_{0}^{1}b(q)D^{q}[frac{x(t)}{f(t,x(t))}]dq=g(t,x(t)),$$ using a fixed point theorem in the Banach algebras. This proof is given in two cases of the continuous and discontinuous function $g$, under the generalized Lipschitz and Caratheodory conditions. | ||
| کلیدواژهها | ||
| Fractional hybrid differential equations؛ Distributed order؛ Extremal solutions؛ Banach algebra | ||
| مراجع | ||
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[1] C. Canuto C, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods in Fluid Dynamic. Englewood Cliffs, NJ: Prentice-Hall, 1998. [2] M. Caputo, Elasticita e Dissipazione, Zanichelli, Bologna, Italy, 1969. [3] M. Caputo, Mean fractional-order-derivatives differential equations and filters, Annali dell universita di Ferrara. Nuova Serie. Sezione VII. Scienze Mathematiche, 41 (1995) 73-84. [4] M. Caputo, Distributed order differential equations modeling dielectric induction and diffusion, Fractional Calculas and Applied Analysis, 4 (2001) 421-442. [5] A. V. Bobyelv and C. Cercignani, The inverse laplace transform of some analytic func- tions with an application to the eternal solutions of the Boltzmann equation, Applied Mathematics Letters, 15(7) (2002) 807-813. [6] B. Davis, Integral Transforms and their applications, 3rd edition, Springer-Verlag, New York, 2001. [7] B. C. Dhage, A nonlinear alternative in Banach algebras with applications to functional differential equations, Nonlinear Functional Analysis and Applications, 8 (2004) 563- 575. [8] B. C. Dhage, Fixed point theorems in ordered Banach algebras and application, Panamerican Mathematical Journal, 9(4) (1999) 93-102. [9] B. C. Dhage, Nonlinear quadratic first order functional integro-differential equation with periodic boundary conditions, Dynamic Systems and Applications, 18 (2009), 303-322. [10] B. C. Dhage, Theorical approximation methods for hybrid differential equations, Dy- namic Systems and Applications, 20 (2011) 455-478. [11] B. C. Dhage, V. Lakshmikantham, Basic results on hybrid differential equations, Non- linear Analysis Hybrid, 4 (2010) 414-424. [12] B. C. Dhage, V. Lakshmikantham, Quadratic perturbations of boundary value problems of second order ordinary differential equations, Differential Equations and Applications, 2(4) (2010) 465-486. [13] S. Heikkila, V. Lakshmikantham, Monotone Iterative Technique For Nonlinear Discon- tinues Differential Equations, Marcel Dekker Inc, New York, 1994. [14] H. Noroozi, A. Ansari, M. Sh. Dahaghin, Existence Results For The Distributed Or- der Fractional Hybrid Differential Equations, Abstract and Applied Analyis, Article ID 163648, 2012. [15] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999. [16] A. Saadatmandi, M. Dehghan, A Legendre collocation method for fractional integro- differential equations, Journal of Vibration and Control, 17(13), (2011) 2050-2058. [17] Y. Zhao, S. Sun, Z. Han, Q. Li, Theory of fractional hybrid differential equations, Computer and Mathematics with Applications, 62 (2011) 1312-1324. | ||
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