One Dimensional Sub-hyperbolic Equation via Sequential Caputo Fractional Derivative

By : Aghalaya S. Vatsala, Yunxiang Bai

Page No: 91-102

Abstract: 
It is well known that the fractional derivative is global in nature compared with integer derivatives. In addition, the fractional dynamic equations represent as better and as more economical models compared with dynamic systems with integer derivative. In this work, we obtain a representation formula for the one dimensional sequential sub hyperbolic linear nonhomogeneous problem with initial and Dirichlet boundary conditions. This is achieved by using the eigenfunction expansion method and Green’s formula. In addition, we have used the Laplace transform method to solve the sequential time derivative dynamic equation. Our result yields the well known integer result as a special case. AMS (MOS) Subject Classification. 34A08, 35C15, 35L04.

Authors :
Aghalaya S. Vatsala
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA.

Yunxiang Bai
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA.
 

DOI: https://doi.org/10.32381/JCISS.2019.44.1-4.6