Work

Backward Continuation of the Solutions of the Cauchy Problem for Linear Fractional System with Deviating Argument

Year: 2024

Type: article

Abstract: Fractional calculus provides tools to model systems with memory effects; when coupled with delays, they model process histories inspired by two independent sources—the memory of the fractional derivative and the impact conditioned by the delays. This work considers a Cauchy (initial) problem for a linear delayed system with derivatives in Caputo’s sense of incommensurate order, distributed delays, and piecewise initial functions. For this initial problem, we study the important problem of the backward continuation of its solutions. We consider the backward continuation of the solutions as a problem of the renewal of a process with aftereffect under given final observation. Sufficient conditions for backward continuation of the solutions of these systems have been obtained. As application, a formal (Lagrange) adjoint system for the studied homogeneous system is introduced, and using the backward continuation, it is proved that for this system there exists a unique matrix solution called by us as the formal adjoint fundamental matrix, which can play the same role as the fundamental matrix in the forward case.

Source: Mathematics

DOI: 10.3390/math13010076

Authors: Hristo Kiskinov, Mariyan Milev, Milena Petkova, Andrey Zahariev

Institutions: Plovdiv University, Sofia University "St. Kliment Ohridski"

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funders: European Commission, NextGenerationEU