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

Qureshi Sania

Journal of Applied Mathematics and Computational Mechanics

2021

Vol. 20, nr 1

83--89

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 ∈ 2 (1;2] and β ∈ 2 (0;1]: The classical mass spring damper model is retrieved for α = β = 1:

The generalized hypergeometric difference equation

Bohner M., Cuchta T.

Demonstratio Mathematica

2018

Vol. 51, nr 1

62--75

A difference equation analogue of the generalized hypergeometric differential equation is defined, its contiguous relations are developed, and its relation to numerous well-known classical special functions are demonstrated.

The Abel summation of the Kontorovich-Lebedev integral representation

Cojuhari P.A., Gomilko A.M.

Opuscula Mathematica

2005

Vol. 25, no. 1

101-107

A new result on the summation of the Kontorovich-Lebedev integral representation in the sense of Abel mean is given.

Special functions related with extremal normalization

Szynal A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2000

z. 24 [181]

137-143

The author studies special functions related with the functional \f(x) - x\ for class of quasiconformal mappings, normalized by conditions f(xn) = Xn.