Received: 7 September 2017
Existence and Hyers-Ulam stability of fractional nonlinear
impulsive switched coupled evolution equations
Department of Mathematics, Guizhou
University, Guiyang, Guizhou 550025, P.R.
Department of Mathematics, University
of Malakand, Dir(L), Khyber
Kamal Shah and Amjad Ali, Department
of Mathematics, University of Malakand,
Dir(L), Khyber Pakhtunkhwa, Pakistan.
Communicated by: S. Georgiev
National Natural Science Foundation of
China, Grant/Award Number: 11661016;
Training Object of High Level and
Innovative Talents of Guizhou Province,
Grant/Award Number: [(2016)4006 ; Unite
Foundation of Guizhou Province,
Grant/Award Number: 7640 ;
Graduate ZDKC, Grant/Award Number:
MSC Classification: 26A33; 34A08; 34A37
In this paper, we study a class of fractional nonlinear impulsive switched cou-
pled evolution equations. Existence and uniqueness of solutions as well as
Hyers-Ulam stability results are presented. An example is provided for the
verification of our results.
fractional, Hyers-Ulam stability, nonlinear impulsive switched systems, solutions
It has been shown that differential equations of fractional order are powerful tools to model the real world problems of
signal processing, viscoelasticity, psychology, control theory, aerodynamics, economics, bioengineering, and networking
more accurately than differential equations of integer order; see, for example, previous studies.
The investigation of
solutions related to toppled systems of differential equations plays an important role in sciences and engineering, because
most of the mathematical models of various problems and phenomenons, particularly in the area of physical biological
and psychological sciences as well as in computer networking.
Recently, evolution-type differential equations of arbitrary order under the nonlocal conditions together with impul-
sive conditions have been given much attention, because such type of equations under the aforementioned conditions
is increasingly using in modeling of the evolution phenomenons that are subject to the abrupt changes in their states.
Numerous applications can be found in the modeling of earth quakes, the preservation of a species through cyclic, sud-
den fluctuations of economy of a state, in absorbent media leakage flow, fluid traffic models dynamic, under impacts
a mechanical systems, stocking, and the heart's actions; see previous studies
for valuable contributions to the
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