# FRACTIONAL DYNAMICAL SYSTEMS FOR VARIATIONAL INCLUSIONS INVOLVING DIFFERENCE OF OPERATORS

Khan, Awais Gul;Noor, Muhammad Aslam;Noor, Khalida Inayat

• Accepted : 2019.01.14
• Published : 2019.03.25
• 140 2

#### Abstract

In the present paper, we propose some new fractional dynamical systems. These dynamical systems are associated with the variational inclusions involving difference of operators problem. The equivalence between the variational inclusion problems and the fixed point problems and as well as the resolvent equations are used to suggest fractional resolvent dynamical systems and fractional resolvent equation dynamical systems, respectively. We show that these dynamical systems converge ${\alpha}$-exponentially to the unique solution of variational inclusion problems under fewer restrictions imposed on operators and parameters. Several special cases also discussed.

#### Keywords

Fractional dynamical systems;Variational inclusions;Difference of operators

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