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Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Rajagopal Joice Nirmala, Krishnan Balachandran (2017)

Kybernetika

This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.

Reliable numerical modelling of malaria propagation

István Faragó, Miklós Emil Mincsovics, Rahele Mosleh (2018)

Applications of Mathematics

We investigate biological processes, particularly the propagation of malaria. Both the continuous and the numerical models on some fixed mesh should preserve the basic qualitative properties of the original phenomenon. Our main goal is to give the conditions for the discrete (numerical) models of the malaria phenomena under which they possess some given qualitative property, namely, to be between zero and one. The conditions which guarantee this requirement are related to the time-discretization...

Remarks concerning Driver's equation

Gerd Herzog, Roland Lemmert (1994)

Annales Polonici Mathematici

We consider uniqueness for the initial value problem x' = 1 + f(x) - f(t), x(0) = 0. Several uniqueness criteria are given as well as an example of non-uniqueness.

Remarks on existence of positive solutions of some integral equations

Jan Ligęza (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We study the existence of positive solutions of the integral equation x ( t ) = μ 0 1 k ( t , s ) f ( s , x ( s ) , x ' ( s ) , ... , x ( n - 1 ) ( s ) ) d s , n 2 in both C n - 1 [ 0 , 1 ] and W n - 1 , p [ 0 , 1 ] spaces, where p 1 and μ > 0 . Throughout this paper k is nonnegative but the nonlinearity f may take negative values. The Krasnosielski fixed point theorem on cone is used.

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