Application of test surfunctions

Abstract

Appropriate definitions and properties are introduced for the scale of Fréchet spaces, . Differentiation of every order is then given for functionals having the space as their domain. These derivatives are similar to Fréchetderivatives. For computational considerations thev are evaluated asf

We then implement some techniques in our setting to solve abroad class of abstract Cauchy problems. The techniques aresimilar to operator techniques employed to classical problems. The order of the operator is introduced as where λ relates to the usual inverse operator to time differentiation and nλ relates to the generalized differentiation which can be associated to spacial differentiation

^†Supported by the Grants-In -Aid Program Faculty of Virginia Commenwealth University

^†Supported by the Grants-In -Aid Program Faculty of Virginia Commenwealth University

Notes

^†Supported by the Grants-In -Aid Program Faculty of Virginia Commenwealth University