General Solution of Two-dimensional Singular Fractional Linear Continuous-Time System Using the conformable derivative and Sumudu transform

Abstract

AbstractThe effectiveness of this paper lies in presenting a new solution for the singular fractional two dimensional linear continuous-time systems using the conformable derivative and Sumudu transform. The proposed technique combines the new advantageous features of conformal derivative and double-delta-Kronecker, which efficiently handles singularities and Sumudu transform, and provides an efficient solution for 2D singular Fornasini-Marchesini fractional models. Applying these approaches, we then derive new explicit expressions for the fundamental matrices of the considered model. The applicability and usefulness of our proposed methods are validated and evaluated by numerical simulations in order to show the accuracy of the obtained results.Keywords: Fractional linear systemsConformable derivativeDouble Laplace transformDouble Sumudu transformFornasini-Marchesini modelsFundamental matrixSingular systemsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgmentsThis paper presents research results of the ACSY-Team (Analysis & Control systems team) and of the doctorial training on the Operational Research from the Pure and Applied mathematics Laboratory UMAB and Decision Support funded by the General Directorate for Scientific Research and Technological Development of Algeria (DGRSDT) and supported by National Higher School of Mathematics (NHSM), University of Mostaganem Abdelhamid Ibn Badis (UMAB) and initiated by the concerted research project on Control and Systems theory (PRFU Project Code C00L03UN270120200003).