GENERALIZATIONS TO SOME INTEGRO-DIFFERENTIAL EQUATIONS EMBODYING POWERS OF A DIFFERENTIAL OPERATOR

Some identification problems for integro - differential operator equations ∗

We consider, in a Hilbert space H, the convolution integro-differential equation u′′(t)−h∗Au(t) = f(t), 0 ≤ t ≤ T , h∗v(t) = ∫ t 0 h(t−s)v(s) ds, where A is a linear closed densely defined (possibly selfadjoint and/or positive definite) operator in H. Under suitable assumptions on the data we solve the inverse problem consisting of finding the kernel h from the extra data (measured data) of the...

L–operator Integro–differential Inequality for Dissipativity of Stochastic Integro–differential Equations

In this paper, Itô stochastic integro-differential equations are considered. By establishing an L -operator integro-differential inequality and using the properties of M -cone and stochastic analysis technique, we obtain some new sufficient conditions ensuring the exponential p -dissipativity of the stochastic integro-differential equations. An example is also discussed to illustrate the effici...

Nonlinear Integro - Differential Equations

Well-posedness and asymptotics of some nonlinear integro-differential equations

We will prove the well-posedness of certain second order ordinary and partial integro-differential equations with an integral term of the form t ∫ 0 m(φ(t−s))φ̇(s) ds, wherem is given and φ is the solution. The new aspect is the dependence of the kernel on the solution. In addition, for the ordinary integro-differential equation, the asymptotic behaviour of the solution is described for some ker...

Fractional type of flatlet oblique multiwavelet for solving fractional differential and integro-differential equations

The construction of fractional type of flatlet biorthogonal multiwavelet system is investigated in this paper. We apply this system as basis functions to solve the fractional differential and integro-differential equations. Biorthogonality and high vanishing moments of this system are two major properties which lead to the good approximation for the solutions of the given problems. Some test pr...