... withvariable delays. Proc Am Math Soc. 136,909–918 (2008)19. Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differentialequationswithvariable delays. NonlinearAnal. ... 200093,ChinaFull list of author information isavailable at the end of the articleAbstractThe linear neutral differential equation withvariable delays is considered in thisarticle. New criteria for ... neutral nonlinear differentialequationswith delay.Nonlinear Anal. 74(12):3926–3933 (2011). doi:10.1016/j.na.2011.02.02917. Raffoul, YN: Stability in neutral nonlinear differentialequations with...
... dimensions with delay. Abstr Appl Anal 2010, 2010:1-16.31. Kilbas AA, Srivastava HH, Trujillo JJ: Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam;2006.32. Krasnoselskii ... systems of higher-order nonlinearfractional differential equations. Fixed Point Theory Appl 2010, 2010:1-17.30. Babakhani A: Positive solutions for systemof nonlinear fractional differentialequations ... for a singular coupled systemof nonlinear fractional differential equations. Appl Math Comput 2004, 150:611-621.25. Su X: Boundary value problem for a coupled systemof nonlinear fractional differential...
... features of advanced models in many areas of application with uncer-tainties are often event-driven. In finance and insurance one has to deal with events such as corporate defaults, operational ... exponential ofa transformed Wiener process, is also an (A ,P)-martingale. From a practical perspective one can say that a martingale issimply a trendless process.Super- and SubmartingalesSystematically ... Financial engineers, quantitative analysts, risk managers, fund managers,insurance professionals and others who have no strong mathematical back-ground and are interested in finance, insurance...
... the same way that one can associate an F[X]-module toany linear transformation ofa vector space over a field F .If∂Y = A 1Y and∂Y = A 2Y are differential equations over k and M1and M2are ... ,yn)Tand A = (a i,j). We notethat there are obvious rules like (AB)= A B + AB, (A −1)= A −1 A A −1and (Ay)= A y + Aywhere A, B are matrices and y is a vector. A linear differential ... analogue for linear differential equations of the classical Galois theory for polynomial equations. The natural analogue of a field in our context is the notion ofa differential field. This is a...
... 3Asmat Ara,1and Nasir-Uddin Khan11Department of Mathematics, University of Karachi, Karachi 75270, Pakistan2Abdul Salam School of Mathematical Sciences, GC University, Lahore, Pakistan3Department ... Theory and A pplications of Fractional Differential Equations, Elsevier, Amsterdam, The Netherlands, 2007.2 R. L. Bagley and R. A. Calico, “Fractional order state equations for the control of viscoelasticallydamped ... aim is to study the mathematical behavior of the solution ut and vt for differentvalues of α. This goal can be achieved by forming Pade’ approximants, which have theadvantage of manipulating...
... with maximaRabha W IbrahimInstitute of Mathematical Sciences, University Malaya, 50603 Kuala Lumpur, MalaysiaEmail address: rabhaibrahim@yahoo.comAbstractIn this article, we employ the Tarski’s ... certain type of fractional differentialequations with maximaAdvances in Difference Equations 2012, 2012:7 doi:10.1186/1687-1847-2012-7Rabha W Ibrahim (rabhaibrahim@yahoo.com)ISSN 1687-1847Article ... Leela, S, Vasundhara, J: Theory of Fractional Dynamic Systems. Cam-bridge Academic Publishers, Cambridge (2009).12 Extremal solutions for certain type of fractionaldifferential equations with...
... statespace. A local linearization technique is applied to nonlinear equations and an approximate linear equation is obtained in(16). A series of values of hidden variable x can be obtainedbased ... information ofa new seizure is available.Thus the system can adaptively update all related parametersautomatically based on available seizure information.From Figure 1, the hidden variable s value ... intracranial EEG data, it has a reliableperformance for all six patients including preictal, interictal,and postictal transition data. Application of our method herefocuses on the same type of...
... I. Albarreal, M.C. Calzada, J.L. Cruz, E. Fern´andez-Cara, M. Mari´n, Stability and Convergence ofa ParallelFractional Step Method for the Solution ofLinear Parabolic Problems, Applied Mathematics ... deals with two fully parallel methods for solving linear partial differential- algebraic equations (PDAEs) of the form:Aut+ B∆u = f(x, t) (1)where A is a singular, symmetric and nonnegative ... interest in the analysis and numerical solution of PDAEsbecause of their importance in various applications, such as plasma physics, magneto hydro dynamics,electrical, mechanical and chemical engineering,...
... and polynomial decay for a quasilinear viscoelastic problem. Nonlinear Anal. 68,785–793 (2007)8. Messaoudi, SA: General decay of solutions ofa viscoelastic equation. J. Math. Anal. Appl. 341, ... Messaoudi, SA, Said-Houari, B: Global nonexistence of positive initial-energy solutions ofasystemof nonlinearviscoelastic wave equationswith damping and source terms. J. Math. Anal. Appl. ... Rammaha, MA: Systems of nonlinear wave equationswith damping and source terms. Diff. Integ. Equ. 19,1235–1270 (2006)23. Said-Houari, B, Messaoudi, SA, Guesmia, A: General decay of solutions of a...