Representations of Solutions of Systems of Time-Fractional Pseudo-Differential Equations

Authors

Sabir Umarov, University of New HavenFollow

Author URLs

Dr. Umarov's Faculty Profile

Document Type

Article

Publication Date

4-2024

Subject: LCSH

Fractional calculus, Pseudodifferential operators, Operator equations--Numerical solutions, Differential equations, Partial

Disciplines

Mathematics

Abstract

Systems of fractional order differential and pseudo-differential equations are used in modeling of various dynamical processes. In the analysis of such models, including stability analysis, asymptotic behaviors, etc., it is useful to have a representation formulas for the solution. In this paper we prove the existence and uniqueness theorems and derive representation formulas for the solution of general systems of fractional multi-order linear pseudo-differential equations through the matrix-valued Mittag-Leffler function. Examples illustrating the obtained results are also provided.

Comments

This article is published in, "Fractional Calculus and Applied Analysis: An International Journal for Theory and Applications," volume 27, issue 2.

DOI

https://doi.org/10.1007/s13540-024-00241-z

Repository Citation

Umarov, Sabir, "Representations of Solutions of Systems of Time-Fractional Pseudo-Differential Equations" (2024). Mathematics Faculty Publications. 21.
https://digitalcommons.newhaven.edu/mathematics-facpubs/21

Publisher Citation

Umarov, S. Representations of solutions of systems of time-fractional pseudo-differential equations. Fract Calc Appl Anal 27, 616–651 (2024). https://doi.org/10.1007/s13540-024-00241-z