POLYNOMIAL OPERATORS, STIELTJES CONVOLUTION, AND FRACTIONAL CALCULUS IN HEREDITARY MECHANICS

Fractional calculus is used to describe the general behavior of materials with memory. An expression for the fractional derivative or the fractional integral is developed in terms of the Stieltjes convolution and the Riesz distribution. The general fractional calculus polynomial operator constitutive equation is reduced to a Stieltjes convolution. A constitutive equation which depends on a memory parameter for an isotropic viscoelastic material is presented.