Semilinear ordinary differential equation coupled with distributed order fractional differential equation

TL;DR

This paper investigates a coupled system of semilinear ordinary differential equations and distributed order fractional differential equations, providing existence and uniqueness results relevant to viscoelasticity modeling and system identification.

Contribution

It introduces a novel analysis of coupled semilinear and distributed order fractional differential equations, including solutions in mild and classical senses, and establishes existence and uniqueness in tempered distributions.

Findings

Existence and uniqueness of solutions for the coupled system.

Application to viscoelasticity and system identification models.

Solutions formulated in mild and classical senses.

Abstract

System of semilinear ordinary differential equation and fractional differential equation of distributed order is investigated and solved in a mild and classical sense. Such a system arises as a distributed derivative model of viscoelasticity and in the system identfica- tion theory. Also, the existence and uniqueness of a solution to a general linear fractional differential equation in the space of tempered distributions is given.