Here, A generates a strongly continuous semi-group in a Banach space X, F(t) is a bounded operator for t âˆˆ J , and f : J Ã— X â†’ X , k : Î” Ã— X â†’ X , g : Î” Ã— X Ã— X â†’ X and h : X p â†’ X are givenâ€¦ (More)

0 g(s, x(s), x(sâˆ’ Ï„(s))) (tâˆ’ s)1âˆ’Î± dÏ‰(s), t âˆˆ J = [0, T ], x(t) = Ïˆ(t), t âˆˆ [âˆ’r, 0], (1.1) where 0 < Î± â‰¤ 1, T > 0 and A is a linear closed operator , defined on a given Hilbert space X . It isâ€¦ (More)

Haussmann in [Journal of mathematical analysis and applications (1978)] discussed asymptotic stability in infinite dimension of the stochastic differential equation * Co E-m 0096-3 doi:10. dX Ã¾ AX dtâ€¦ (More)

Numerical solution of stochastic delay differential equations is studied by using explicit one-step methods. One-step method is asymptotically zero-stable in the quadratic mean square sense.

Existence and controllability results for nonlinear Hilfer fractional differential equations are studied. Sufficient conditions for existence and approximate controllability for Sobolev-typeâ€¦ (More)

The ionization and appearance energies for the molecular and fragment ions, respectively, of the three dimethylaniline isomers are reported. Breakdown graphs have been constructed expressing theâ€¦ (More)