Sub Hyperbolic Linear Partial Fractional Differential etc

Abstract

Using the eigenfunction expansion method we obtain a representation form for the solution of the linear non homogenous sub hyperbolic fractional Caputo fractional partial differential equation in one dimensional space. The solution obtained depends on the nonhomogeneous terms of the equation and the initial and boundary conditions. Here we consider the $q^{th}$ order fractional differential equation in time variable for $1<q<2.$ Results when $0<q<1$ can be obtained as a special case of the results obtained here.  The software MAPLE 16 is used to graphically represent solutions to some linear non homogenous sub hyperbolic fractional Caputo fractional partial differential equation in one dimensional space.