There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Fractional Differential Equations

Stochastic equations in infinite dimensions

Computer Methods in Applied Mechanics and Engineering

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Nonlinear Functional Analysis And Its Applications

L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem

Existence of positive weak solutions for a class of Kirrchoff elliptic systems with multiple parameters: Existence of positive weak solutions for a class of Kirrchoff elliptic systems with multiple parameters

This paper studies the dynamics of a new fractional-order map with no fixed points. Through phase plots, bifurcation diagrams, largest Lyapunov exponent, it is shown that the proposed fractional map exhibit chaotic and periodic behavior. New Hidden chaotic attractors are observed, and transient state is found to exist. Complexity of the new map is also analyzed by employing approximate entropy. Results, show that the fractional map without fixed point have high complexity for certain fractional order. In addition, a control scheme is introduced. The controllers stabilize the states of the fractional map and ensure their convergence to zero asymptotically. Numerical results are used to verify the findings.

A fractional map with hidden attractors: chaos and control

The finite element approximation of evolutionary Hamilton–Jacobi–Bellman equations with nonlinear source terms

In this paper, a class of nonlinear viscoelastic Kirchhoff equation in a bounded domain with a time-varying delay in the weakly nonlinear internal feedback is considered, where the global existence of solutions in suitable Sobolev spaces by means of the energy method combined with Faedo–Galerkin procedure is proved with respect to the condition of the weight of the delay term in the feedback and the weight of the term without delay and the speed of delay. Furthermore, a general stability estimate using some properties of convex functions is given.

Salah Boulaaras

Papers

L∞-asymptotic behavior for a finite element approximation in parabolic quasi-variational inequalities related to impulse control problem

Existence of positive weak solutions for a class of Kirrchoff elliptic systems with multiple parameters: Existence of positive weak solutions for a class of Kirrchoff elliptic systems with multiple parameters

A fractional map with hidden attractors: chaos and control

The finite element approximation of evolutionary Hamilton–Jacobi–Bellman equations with nonlinear source terms

Global Existence and Decay of Solutions for a Class of Viscoelastic Kirchhoff Equation