Asymptotic behavior of solutions of linear multi-order fractional differential systems

Abstract In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of linear multi-order fractional differential equation systems.

[1]  G. H. Erjaee,et al.  Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations , 2013 .

[2]  Kai Diethelm,et al.  Multi-term fractional differential equations, multi-order fractional differential systems and their numerical solution , 2008 .

[3]  I. Podlubny.  Fractional differential equations , 1998 .

[4]  Yin Yang,et al.  Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method , 2013, Applied Mathematics.

[5]  Yuanlu Li,et al.  Solving a nonlinear fractional differential equation using Chebyshev wavelets , 2010 .

[6]  Kai Diethelm,et al.  A fractional calculus based model for the simulation of an outbreak of dengue fever , 2013 .

[7]  W. Ames.  Mathematics in Science and Engineering , 1999 .

[8]  Aiguo Xiao,et al.  Computers and Mathematics with Applications Convergence of the Variational Iteration Method for Solving Multi-order Fractional Differential Equations , 2022 .

[9]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .

[10]  Multi-term fractional differential equations with nonlocal boundary conditions , 2018, Open Mathematics.

[11]  R. Gorenflo,et al.  Mittag-Leffler Functions, Related Topics and Applications , 2014, Springer Monographs in Mathematics.

[12]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[13]  K. Diethelm.  The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[14]  Esmail Hesameddini,et al.  Numerical solution of multi-order fractional differential equations via the sinc collocation method , 2015 .

[15]  N. D. Cong,et al.  On stable manifolds for planar fractional differential equations , 2014, Appl. Math. Comput..

[16]  Jürgen Kurths,et al.  Equivalent system for a multiple-rational-order fractional differential system , 2013, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[17]  Tridip Sardar,et al.  The analytical approximate solution of the multi-term fractionally damped Van der Pol equation , 2009 .

[18]  J. B. Stankovic,et al.  FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES , 2007 .

[19]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[20]  Kai Diethelm,et al.  Multi-order fractional differential equations and their numerical solution , 2004, Appl. Math. Comput..

[21]  Hossein Jafari,et al.  Solving a multi-order fractional differential equation using adomian decomposition , 2007, Appl. Math. Comput..

[22]  Gennadi Vainikko.  Which Functions are Fractionally Differentiable , 2016 .

[23]  A. E. M. El-Mesiry,et al.  Numerical solution for multi-term fractional (arbitrary) orders differential equations , 2004 .

[24]  A. Wiman,et al.  Über die Nullstellen der FunktionenEa(x) , 1905 .

[25]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[26]  N. Sweilam,et al.  Numerical studies for a multi-order fractional differential equation , 2007 .

[27]  Weihua Deng,et al.  ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH MULTI-ORDERS , 2007 .

[28]  Francesco Mainardi,et al.  The Classical Mittag-Leffler Function , 2020, Springer Monographs in Mathematics.

[29]  Jinhu Lü,et al.  Stability analysis of linear fractional differential system with multiple time delays , 2007 .

[30]  Ahmed M. A. El-Sayed,et al.  Numerical methods for multi-term fractional (arbitrary) orders differential equations , 2005, Appl. Math. Comput..