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Faltung equations (closed cycle type) have a wide range of biological applications, nonetheless, they are poorly studied. We use a Volterra‐Kostitzin model (which is a Faltung equation) to study the dynamics of a certain species, where the integral term represents a residual action. The complexity of resolution of this non‐linear equation using classical numeric methods is here solved with the Adomian decomposition method. Our method provides the same graphic solution as others do, such as the numeric method Miladie. However, the decomposition method of Adomian has the advantage that neither time nor space are considered discontinuous and that it gives an analytical solution with a reliable approximation.