In this manuscript, we analyze the solution for class of linear and nonlinear Caputo fractional Volterra Fredholm integro-differential equations with time varying delay. Also, demonstrate stability analysis these equations. Our paper provides a convergence semi-analytical approximate method It would be desirable to point out results.

The paper deals with semigroups of operators associated with delay differential equation: ẋ(t) = Ax(t) + L1x(t− h) + L2xt, where A is the infinitesimal generator of an analytic semigroup on a Hilbert space X and L1, L2 are densely defined closed operators in X and L2(−h, 0;X) respectively. The adjoint semigroup of the solution semigroup of the delay differential equation is characterized. Eigen...

STABILITY DOMAIN OF LINEAR DIFFERENTIAL EQUATION WITH TWO DELAYS I.S. Levitskaya e–mail: [email protected] Chelyabinsk State Pedagogical University, Chelyabinsk, Russia We study the stability of the zero solution of the differential equation = − − τ − − τ where τ τ ∈ τ ≥ τ ≥ By means of numerical experiments we constructed the stability domains of this equation in space of parameters  for any re...

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as usual. In more general cases, the right hand side of the differential equation contains more arguments. It also happens that the delay is given only implicitly by an equation which involves the history xt of the state. Differential equations with state-dependent delay share the property that the results on the uniqueness and dependence on initial data from the theory of retarded functional d...