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- S. A. Belbas
- Applied Mathematics and Computation
- 2007

We formulate and analyze a new method for solving optimal control problems for systems governed by Volterra integral equations. Our method utilizes discretization of the original Volterra controlled system and a novel type of dynamic programming jn which the Hamilton-Jacobi function is parametrized by the control function (rather than the state, as in the… (More)

- S. A. Belbas, W. H. Schmidt
- Applied Mathematics and Computation
- 2005

- S. A. Belbas
- Applied Mathematics and Computation
- 2008

- S. A. Belbas, W. H. Schmidt
- Applied Mathematics and Computation
- 2009

We obtain necessary conditions of optimality for impulsive Volterra integral equations with switching and impulsive controls, with variable impulse time-instants. The present work continues and complements our previous work on impulsive Volterra control with fixed impulse times.

- S. A. Belbas
- Applied Mathematics and Computation
- 2006

We derive formulae for the calculation of Taylor coefficients of solutions to systems of Volterra integral equations, both linear and nonlinear, either without singularities or with singularities of Abel type and logarithmic type. We also obtain solutions to certain systems of Volterra equations of the first kind. In all cases except the case of logarithmic… (More)

- S. A. Belbas
- Applied Mathematics and Computation
- 2013

- S. A. Belbas, Yuriy Bulka
- Applied Mathematics and Computation
- 2011

- S. A. Belbas
- Applied Mathematics and Computation
- 2008

- S. A. Belbas
- Applied Mathematics and Computation
- 2007

- S. A. Belbas
- Applied Mathematics and Computation
- 2005

We define two models of hysteresis that generalize the Preisach model. The first model is deterministic, the second model is stochastic and it utilizes discontinuous transition probabilities that satisfy impulsive differential equations. For the first model we prove, among other things, a local version of the "wiping out" property; for the stochastic model,… (More)