Volterra integro-differential equation

Using the standard memory function techniques (Chapters I and IV), we have that Oo(l) satisfies the Volterra integro-differential equation... 

To establish the relation between the memory function formalism and the moments, consider the Volterra integro-differential equations (3.44) for %it) ... 

The procedure can be iterated, considering now the Volterra integro-differential equation (3.44) for x(/), then for 2(0. and so on. The implications of Eq. (3.54) have been discussed in more detail in Chapter III, with comments on product-difference (PD) algorithms. 

V Volterra. Theory of Functionals and Integro-Differential Equations. Dover, New York, NY, 1959. 

W2. Whittaker, E. T., in Theory of Functionals and of Integral and Integro-Differential Equations (V. Volterra), pp. 5-28. Dover, New York, 1959. 

The system (10.1) can be considered as a nonlinear system of Volterra type integro-differential equations with finite aftereffect. 

As shown by Vuitovich and Nurzhanov (1982), for the systems of integro-differential equations of the Volterra type with infinite aftereffect, one can also formulate and prove the statements similar to the theorem given above. Here we present one of these statements. 

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