Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform

Abstract

. Closed form solutions for mathematical systems are not easy to find in many cases. In particular, linear systems such as the population growth/decay model, RLC circuit, mixing problems in chemistry, first-order kinetic reactions, and mass spring damper system in mechanical and mechatronic engineering can be handled with tools available in theoretical study of linear systems. One such linear system has been investigated in the present research study. The second order linear ordinary differential equation called the mass spring damper system is explored under the Caputo type differential operator while using the Sumudu integral transform. The closed form solution has been found in terms of the Fox H-function wherein different aspects of the solution can be obtained with variation in α ∈ ( 1 , 2 ] and β ∈ ( 0 , 1 ] . The classical mass spring damper model is retrieved for α = β = 1 . MSC 2010: 26A33, 34M03.