Nuri Ozalp

A fractional order SEIR model with vertical transmission

In this paper, we introduce a fractional order SEIR model with vertical transmission within a nonconstant population. We show that the model introduced in this paper has nonnegative solutions. We give a detailed analysis for the asymptotic stability of disease free and positive fixed points. Numerical simulations are also presented to verify the obtained results.

A fractional order nonlinear dynamical model of interpersonal relationships

In this paper, a fractional order nonlinear dynamical model of interpersonal relationships has been introduced. The stability of equilibrium points is studied. Numerical simulations are also presented to verify the obtained results.

The quenching behavior of a nonlinear parabolic equation with a singular boundary condition

In this paper, we study the quenching behavior of solution of a nonlinear parabolic equation with a singular boundary condition. We prove finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions. Furthermore, we show that the time derivative blows up at quenching point. Also, we get a lower solution and an upper bound for quenching time. Finally, we get a quenching rate and lower bounds for quenching time.

The quenching behavior of a semilinear heat equation with a singular boundary outflux

In this paper, we study the quenching behavior of the solution of a semilinear heat equation with a singular boundary outflux. We prove a finite-time quenching for the solution. Further, we show that quenching occurs on the boundary under certain conditions and we show that the time derivative blows up at a quenching point. Finally, we get a quenching rate and a lower bound for the quenching time.

Analysis of a fractional-order couple model with acceleration in feelings.

A fractional-order nonlinear dynamical model of couple has been introduced. Upper bounds are obtained for a fractional-order nonlinear dynamical model. Also different from other models, a model with the order 2α is discussed. We are expecting an acceleration in feelings; that is why we increase the order of the derivative between 1 < 2α ≤ 2. Stability analysis of the fractional-order nonlinear dynamical model of involving two persons is studied using the fractional Routh-Hurwitz criteria. By using stability analysis on fractional-order system, we obtain sufficient condition on the parameters for the locally asymptotic stability of equilibrium points. Finally, numerical simulations are presented to verify the obtained results.

A computational method for hypersurfaces in terms of gamma function

A general volume formula in terms of beta–gamma functions for a wide range of symmetric solids is established and a program code for computational purposes is generated. 2004 Elsevier Inc. All rights reserved.

Fractional Laplace transform method in the framework of the CTIT transformation

We propose an adapted Laplace transform method that gives the solution of a linear fractional differential equation with constant coefficients in terms of exponential function. After we mention what the utilized transformation, the CTIT transformation, is based on, we explain how it can reduce the problem from fractional form to ordinary form when it is used with Laplace transformation, via some examples for 0<<2 where is the order of fractional derivative. Finally, we illustrate the applications of our results.

Radial-type complete solutions for a class of partial differential equations

We give some fundamental solutions of a class of iterated elliptic equations including Laplace equation and its iterates.