Solutions For Fractional Linear Systems With Hattaf Derivative

Sermin Öztürk; Rabia  Solak

doi:10.24297/jam.v22i.9550

Authors

Sermin Öztürk Department of Mathematics( Afyon Kocatepe University, Faculty of Science and Literature, Afyonkarahisar 03200, Turkey)
Rabia Solak Department of Mathematics( Afyon Kocatepe University, Institue of Science, Afyonkarahisar 03200, Turkey)

DOI:

https://doi.org/10.24297/jam.v22i.9550

Keywords:

analytical solution, Hattaf derivative, linear system

Abstract

This paper deals with the analytical solutions of the fractional-order linear systems characterized by DX(t) = AX(t)
fractional differential equations. Here D, is the fractional derivative in the Hattaf sense and A is the (2x2)-type
non-singular real coefficient matrix. We present some results related to the existence of analytical solutions of the linear
equation systems of the Hattaf fractional derivative. These solutions are provided for three different fractional-order
linear systems.

Downloads

Download data is not yet available.

References

Caputo, M.; Mauro, F. A new definition of fractional derivative without singular kernel. Progress in Fractional Diff. and Appl. 2015, 1, 2, 73-85.

Hattaf, K. A new generalized definition of fractional derivative with non-singular kernel. Computation. 2020, 8, 49, 1-9.

Atangana, A.; Baleanu, Dumitru, B. New fractional derivatives with nonlocal and non-singular kernel: Theory and application to heat transfer model. Thermal Science. 2016, 20, 763-769.

Al-Refai, M. On weighted Atangana–Baleanu fractional operators. Adv. Differ. Eq. 2020, 2020, 3, 1-11.

Ross, B. Fractional Calculus and its Applications ;Lecture Notes in Mathematics, Springer-Verlag: Berlin, 1975.

Podlubny, I. Fractional-Order Systems and Fractional-Order Controllers; Slovak Academy of Sci. Ins. of Exp. Physics, University of Technology: Kosic, 1994.

Wang, S.; Juan, Liu; Xindong, Z. Properties of solutions for fractional-order linear system with differential equations. AIMS Mathematics. 2022, 7, 8 , 15704-15713.

Wei, Y. Q.; Da-Yan, L.; Driss, B. Innovative fractional derivative estimation of the pseudo-state for a class of fractional order linear systems. Automatica. 2019, 99, 157-166.

Hattaf, K. On some properties of the new generalized fractional derivative with non-singular kernel. Mathematical

Problems in Engineering, 2021, 2021, 1580396 .