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Mittag-Leffler stability for a Timoshenko problem

Tatar Nasser-eddine

International Journal of Applied Mathematics and Computer Science

2021

Vol. 31, no. 2

219--232

A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.

Approximation solvability for a system of implicit nonlinear variational inclusions with H-monotone operators

Kim J. K., Bhat M. I.

Demonstratio Mathematica

2018

Vol. 51, nr 1

241--254

In this paper, we introduce and study a new system of variational inclusions which is called a system of nonlinear implicit variational inclusion problems with A-monotone and H-monotone operators in semi-inner product spaces. We define the resolvent operator associated with A-monotone and H-monotone operators and prove its Lipschitz continuity. Using resolvent operator technique, we prove the existence and uniqueness of solution for this new system of variational inclusions. Moreover, we suggest an iterative algorithm for approximating the solution of this system and discuss the convergence analysis of the sequences generated by the iterative algorithm under some suitable conditions.

On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

Yan Z.

Opuscula Mathematica

2012

Vol. 32, no. 2

377-394

In this paper, we discuss the existence results for a class of nonlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.