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

Volume 5, Issue 6, pp 448--458
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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

Keywords

• Infinite linear systems of differential equations
• systems of linear equations
• Laplace operator.

•  40C05
•  44A10

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