Solvability of infinite differential systems of the form \(x' (t) =Tx(t)+b\) where \(T\) is either of the triangles \(C(\lambda)\) or \(\overline{N}_ q\)


Authors

Ali Fares - Équipe Algèbre et Combinatoire, EDST, Faculté des sciences-- Section 1, Université libanaise, Hadath, Liban. Ali Ayad - Équipe Algèbre et Combinatoire, EDST, Faculté des sciences--Section 1, Université libanaise, Hadath, Liban.


Abstract

In this paper, we are interested in solving infinite linear systems of differential equations of the form \(x' (t) = Tx (t) + b\) with \(x(0) = x_0\); where \(T\) is either the generalized Cesàro operator \(C (\lambda)\) or the weighted mean matrix \(\overline{N}_ q, x_0\) and b are two given infinite column matrices and \(\lambda\) is a sequence with non-zero entries. We use a new method based on Laplace transformations to solve these systems.


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ISRP Style

Ali Fares, Ali Ayad, Solvability of infinite differential systems of the form \(x' (t) =Tx(t)+b\) where \(T\) is either of the triangles \(C(\lambda)\) or \(\overline{N}_ q\), Journal of Nonlinear Sciences and Applications, 5 (2012), no. 6, 448--458

AMA Style

Fares Ali, Ayad Ali, Solvability of infinite differential systems of the form \(x' (t) =Tx(t)+b\) where \(T\) is either of the triangles \(C(\lambda)\) or \(\overline{N}_ q\). J. Nonlinear Sci. Appl. (2012); 5(6):448--458

Chicago/Turabian Style

Fares, Ali, Ayad, Ali. "Solvability of infinite differential systems of the form \(x' (t) =Tx(t)+b\) where \(T\) is either of the triangles \(C(\lambda)\) or \(\overline{N}_ q\)." Journal of Nonlinear Sciences and Applications, 5, no. 6 (2012): 448--458


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