iosr-Jm   Volume-10 ~ Issue-6 ~ Nov-Dec 2014

Abstract: In this paper, we implement Adomian decomposition method for solving numerically non-linear delay differential equations of fractional order. The fractional derivative will be in the Caputo sense. In this approach, the solutions are found in the form of a convergent power series with easily computed components. Some numerical examples are presented to illustrate the accuracy and ability of the proposed method.

Keywords: Adomian decomposition method, delay differential equations, fractional calculus, fractional delay differential equations.

[1] KilbasA.A., Srivastara H.M. and TrujilloJ.J., ''Theory and applications of Fractional Differential Equations'', ELSEVIER 2006.
[2] MoragdoM.L., Ford N. J. and Lima P.M.,''Analysis and numerical methods for fractional differential equations with delay'', Journal of computational and applied mathematics 252(2013) 159-168.
[3] LakshmikanthamV., ''Theory of fractional functional differential equations'', J.NonlinearSci. 69 (2008) 3337-3343.
[4] Ye H., Ding Y. andGao.J.,''Theexistence of positive solution of Dα x t −x 0 =x t f t,xt '', positivity 11(2007) 341-350.
[5] Liao C. and Ye H., ''Existence of positive solutions of nonlinear fractional delay differential equations",positivity 13 (2009) 601-609.

Abstract: In this article, the effect of variable prestress on the behavior of thin beam on constant elastic foundation is presented. The moving load is distributed over the entire span of the beam and governs by fourth order partial differential equation. It is shown from the numerical analysis that the higher values of axial force N , the lower the amplitude response of the beam with variable prestress. The same argument goes for foundation rigidity b K . Results in plotted curves indicate that resonance is reached earlier in moving mass solution than moving force solution.
Keywords: Distributed load, Prestress, Resonance, Response, Thin beam.

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93),1971,1003-1006.
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Winkler elastic foundation, Journal of the Nigerian Association of Mathematical Physics,(9), 2005, 151-162.
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International Journal of Applied Science and Technology, 2(6), 2012.
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1967).

Abstract: In this paper we present the Painlevè test for the (1+1) –dimensional travelling regularized long wave (TRLW) equation, the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation, the modified improved Kadomtsev-Petviashvili equation (MIKP) and the variant shallow water wave equations. The associated Bäcklund transformations are obtained directly from the Painlevè test.
Keywords: the (1+1) –dimensional travelling regularized long wave (TRLW) equation, the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation, the modified improved Kadomtsev-Petviashvili equation (MIKP), the variant shallow water wave equations and Painlevè analysis.� 𝐿 satisfying

[1]. V. O. Vakhnenko, E. J. Parkes and A. J. Morrison, A Bäcklund transformation and the inverse scattering transform method
for the generalised Vakhnenko equation, Chaos, Solitons& Fractals, 17(2003) 683–92.
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University (1991).
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Lett. 19 (1967)1095–1102.
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Problems I (1985) 193-198.
[5]. C. Yong, L. Biao, and Z. Hong-Qing, B¨acklund Transformation and Exact Solutions for a New Generalized Zakharov
Kuzentsov Equation with Nonlinear Terms of Any Order, Commun.Theor. Phys. 39 (2003)135–140.

Abstract: Let G= ( V , E ) be a simple connected graph. A set S V is a total dominating set of G if every vertex is adjacent to an element of S. Let Dt(Wn2,i) be the family of all total dominating sets of the graph Wn2, n ≥ 3 with cardinality i, and let dt (Wn2,i) = │Dt (Wn2 , i) │. In this paper we compute dt(Wn2,i),and obtain the polynomial Dt(Wn2, x) = 𝑑𝑡(𝑊𝑛2,𝑖)𝑥𝑖𝑛+1i=Υt(Wn2), which we call total domination polynomial of Wn2, n ≥3 and obtain some properties of this polynomial.

Keywords: square of wheel, total domination set, total domination polynomial

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Abstract: We develop a deterministic model to understand the underlying dynamics of HBV infection at population level. The model, which incorporates the vaccination and treatment of individuals, the re-infections of latent, carrier and recovery individuals, is rigorously analyzed to gain insight into its dynamical features. The mathematical analysis reveals that the model exhibits a backward bifurcation. This phenomenon resulted due to the exogenous re-infection of HBV disease . It is shown that, in the absence of such re-infection, the model has a disease-free equilibrium (DFE) which is globally asymptotically stable (GAS) using Lyapunov function and LaSalle Invariance Principle whenever the associated reproduction threshold is less than unity. Further, the model has a unique endemic equilibrium(EEP), for a special case, whenever the associate threshold quantity exceeds unity. This EEP is shown to be GAS, for a special case, using a non-linear Lyapunov function of Goh-Volterra type.

Keywords: Hepatitis B virus (HBV), basic reproduction number, equilibria, stability, Lyapunov function, transmission dynamics, disease endemic equilibrium.

[1]. A.S. Perelson, A. U. Neumann, M. Markowitz (1996). HIV-1 dynamics in vivo: Virion clearance rate, infested cell lifespan and
viral generation time, Science Vol 271, pp: 1582-1586.
[2]. Ahmad N, Alam S, Mustafa G, Adnan AB, Baiq RH, Khan M (2008). e-antigen-negative chronic hepatitis B in Bangladesh.
Hepatobiliary Pancreat Dis Int. Vol 7, No 4, pp:379-82.
[3]. Castillo-Chavez, C. and B. Song (2004).Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. Vol 1, No. 2,
pp: 361-404.
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Carcinoma with Hepatitis B Virus Infection: Bangladesh Perspective. Journal of Chittagong Medical College Teaches Association.
Vol 20, No.1, pp: 31-33.
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and risk factors. International Journal of Epidemiology; Vol 30, pp: 878-884.

Abstract: Government budgets continue to increase over the years. This is partly due to increasing health issues and ways of eradicating health hazards, and partly due to capital intensive projects. This research work is carried out on the number of reported cases and deaths resulting from tuberculosis. A period of 20 years (1988 to 2007) is considered. A time series analysis performed on this data reveals that tuberculosis infection has been on the rise over the years. The situation is also the same for the number of deaths. A suitable forecast is carried out using appropriate and reliable method which also indicates increase in the two related populations (reported cases and deaths) under study.

Keywords: Epidemic, Infectious Diseases, Morbidity, Tuberculosis

[1]. Mark Cichocki R.N., Re-emergence of an Old Epidemic www.wrongdiagnosis.com accessed Oct. 2007.
[2]. World Health Organization, Global Tuberculosis Control Surveillance,Planning,Financing: WHO report 2006. WHO/HTM/TB/2006, 362. Geneva: WHO, 2006.
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Abstract: It is well known that fraction (𝑎/𝑏) can be expressed as the sum of N unit fractions. Such representations are known as Egyptian fractions. In practice, each 𝑎/𝑏 can be expressed by several different Egyptian fraction expansions. In this paper we present a generalized expression for 3/𝑛 where 𝑁=3 for all positive integers 𝑛. Under mind assumptions convergence results has been established.

Keywords: Egyptian Fraction, Unit Fraction, Shortest Egyptian Fraction

[1]. Dr. Ron Knott, (1996-2014) Egyptian fractions, website: http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fractions/egyptian.html (last updated April,2014)
[2]. Gay, R., C. Shute, the Rhind Mathematical Papyrus: an Ancient Egyptian Text, "British Museum Press, London", 1997.
[3]. Olga KOSHELEVA and Vladik KREINOVICH, Egyptian Fraction Revisited "Informatics in Education", 2009, Vol. 8, No. 1, 35–48
[4]. Simon Brown, Bounds of the denominator of Egyptian Fractions "World Applied Programming" Vol (2), Issue (9), September 2012. 425-430 ISSN: 2222-2510copyright 2012 WAP journal
[5]. Tieling Chen and Reginald Koo. Two term Egyptian fraction "Number Theory and Discrete Mathematics" Vol. 19, 2013, No. 2, 15–25

Abstract: The major shortcomings of Classical Newton's method for nonlinear equations entail computation of Jacobian matrix and solving systems of n linear equations in every iteration. Mostly function derivatives are quit costly and Jacobian is computationally expensive which requires storage of matrix in each iteration. The appealing approach is based on Fixed Newton's but the method mostly requires high number of iteration as the dimension of the systems increases due to less Jacobian information in every iteration. In this paper, we introduce a new procedure via two-step scheme that will reduce the well known shortcomings of Fixed and classical Newton methods. Numerical experiments are carried out which shows that, the proposed method is very encouraging are presented.
Keywords: Nonlinear equations, Equations, Fixed Newton's, Inverse Jacobian.

[1]. M.Y. Waziri and Z. A. Majid, 2012A new approach for solving dual Fuzzy nonlinear equations, Advances in Fuzzy Systems. Volume 2012, Article ID 682087, 5 pages doi:10.1155/2012/682087 no. 25, 1205 - 1217.
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[3]. C.T. Kelley Iterative Methods for Linear and Nonlinear Equations", SIAM, Philadelphia,
[4]. M. Y. Waziri, W.J. Leong, M. A. Hassan,M. Monsi, A New Newton method with diagonal Jacobian approximation for systems of Non-Linear equations. Journal of Mathematics and Statistics Science Publication.6 :(3) 246-252 (2010).
[5]. M.Y. Waziri, W.J. Leong, M.A. Hassan, M. Monsi, Jacobian computation-free New- ton method for systems of Non-Linear equations. Journal of numerical Mathematics and stochastic. (2010); 2 :1 : 54-63.