We consider fractional hybrid differential equations involving the Caputo fractional derivative of order 0 < α < 1. Using fixed point theorems developed by Dhage et al. in Applied Mathematics Letters 34, 76-80 (2014), we prove the existence and approximation of mild solutions. In addition, we provide a numerical example to illustrate the results obtained. Primary 34A08; secondary 34A38; 34A45
MSC:
We study the existence and monotone iterative approximation of mild solutions of fractional-order neutral differential equations involving a generalized fractional derivative of order
0
<
α
<
1
which can be reduced to Riemann–Liouville or Hadamard fractional derivatives. The existence of mild solutions is obtained via fixed point techniques in a partially ordered space. The approach is constructive and can be applied numerically. In particular, we construct a monotone sequence of functions converging to a solution which is illustrated by a numerical example.
This paper studies the dynamics of an opinion formation model with a leader associated with a system of fractional differential equations. We applied the concept of
α
-exponential stability and the uniqueness of equilibrium to show the consensus of the followers with the leader. A sufficient condition for the consensus is obtained for both fractional formation models with and without time-dependent external inputs. Moreover, numerical results are provided to illustrate the dynamical behavior.
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