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Numerical approach to the controllability of fractional order impulsive differential equations

Kumar Avadhesh, Vats Ramesh K., Kumar Ankit, Chalishajar Dimplekumar N.

Demonstratio Mathematica

2020

Vol. 53, nr 1

193--207

In this manuscript, a numerical approach for the stronger concept of exact controllability (total controllability) is provided. The proposed control problem is a nonlinear fractional differential equation of order α ∈ (1, 2] with non-instantaneous impulses in finite-dimensional spaces. Furthermore, the numerical controllability of an integro-differential equation is briefly discussed. The tool for studying includes the Laplace transform, the Mittag-Leffler matrix function and the iterative scheme. Finally, a few numerical illustrations are provided through MATLAB graphs.

Generalizations of two-index two-variable Hermite matrix polynomials

Metwally M., Mohamed M., Shehata A.

Demonstratio Mathematica

2009

Vol. 42, nr 4

687-701

In this paper, we introduce a new generalization of the Hermite matrix polynomials expansions of some relevant matrix functions appearing in the solution of differential systems. An explicit representation and an expansion of the matrix exponential in a series of these matrix polynomials is obtained. Properties of Hermite matrix polynomials such as the recurrence formula permit an efficient computations of matrix functions are established. A new expansions of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed.