mohammad hossein akrami | Yazd University (original) (raw)

Papers by mohammad hossein akrami

Mathematical Researches, May 10, 2021

Iranian journal of mathematical chemistry, Mar 1, 2021

International Journal of Nonlinear Analysis and Applications, 2021

In this article, we are going to study the stability and bifurcation of a two-dimensional discret... more In this article, we are going to study the stability and bifurcation of a two-dimensional discrete time vocal fold model. The existence and local stability of the unique fixed point of the model is investigated. It is shown that a Neimark-Sacker bifurcation occurs and an invariant circle will appear. We give sufficient conditions for this system to be chaotic in the sense of Marotto. Numerically it is shown that our model has positive Lyapunov exponent and is sensitive dependence on initial conditions. Some numerical simulations are presented to illustrate our theoretical results.

$Research paper thumbnail of Hopf and forward bifurcation of an integer and fractional-order SIR epidemic model with logistic growth of the susceptible individuals$

Journal of Applied Mathematics and Computing, 2020

This paper deals with the qualitative behavior of an integer and fractional-order SIR epidemic mo... more This paper deals with the qualitative behavior of an integer and fractional-order SIR epidemic model with logistic growth of the susceptible individuals. Firstly, the positivity and boundedness of solutions for integer-order model are proved. The basic reproduction number R 0 is driven and it is shown that the disease-free equilibrium is globally asymptotically stable if R 0 < 1 in integer-order model. Using the methods of bifurcations theory, it is proved that the integer-order model exhibits forward bifurcation and Hopf bifurcation. Next, with the aim of the stability theory of fractional-order systems, some conditions, which can guarantee the local stability of the fractionalorder model, are developed and occurrence of forward and Hopf bifurcations in this model are studied. Lastly, numerical simulations are illustrated to support the theoretical results and a comparison between the integer and fractional-order systems is presented.

Communications in Nonlinear Science and Numerical Simulation, 2019

In this paper, the stability and bifurcation in a class of stochastic vocal folds dynamical model... more In this paper, the stability and bifurcation in a class of stochastic vocal folds dynamical model are investigated. We use polar coordinate, Taylor expansion and stochastic averaging method to transform our classic system into an Itô averaging diffusion system. Also, we recall some theorems that give us some conditions which leads to sufficient conditions on drift and diffusion coefficients for stochastic stability and P-bifurcation of the model. Finally, numerical simulations are presented to show the effects of the noise intensity and illustrate our theoretical results.

International Journal of Biomathematics, 2017

A two-parameter family of discrete models, consisting of two coupled nonlinear difference equatio... more A two-parameter family of discrete models, consisting of two coupled nonlinear difference equations, describing a host–parasite interaction is considered. In particular, we prove that the model has at most one nontrivial interior fixed point which is stable for a certain range of parameter values and also undergoes a Neimark–Sacker bifurcation that produces an attracting invariant curve in some areas of the parameter.

Fractional Calculus and Applied Analysis, 2015

In this article, we have implemented reconstruction of variational iteration method as a new appr... more In this article, we have implemented reconstruction of variational iteration method as a new approximate analytical technique for solving fractional Black-Scholes option pricing equations. Indeed, we essentially use the well-known Mittag-Leffler function to obtain explicit solutions for some examples of financial mathematics equations.

$Research paper thumbnail of Chebyshev operational matrix method for solving multi-order fractional ordinary differential equations$

Applied Mathematical Modelling, 2013

Abstract The aim of this article is to present an analytical approximation solution for linear an... more Abstract The aim of this article is to present an analytical approximation solution for linear and nonlinear multi-order fractional differential equations (FDEs) by extending the application of the shifted Chebyshev operational matrix. For this purpose, we convert FDE into a counterpart system and then using proposed method to solve the resultant system. Our results in solving four different linear and nonlinear FDE, confirm the accuracy of proposed method.

Communications in Mathematical Biology and Neuroscience, 2018

In this paper, local dynamics of a three-dimensional host parasite model as a discrete dynamical ... more In this paper, local dynamics of a three-dimensional host parasite model as a discrete dynamical system has been studied. The existence of fixed points and stability behaviour near these points are investigated. By use of centre manifold theorem we describe the stability of non-hyperbolic fixed points. Some numerical simulations explain our theoretical results in better way.

Chaos: An Interdisciplinary Journal of Nonlinear Science

The slogan “nobody is safe until everybody is safe” is a dictum to raise awareness that in an int... more The slogan “nobody is safe until everybody is safe” is a dictum to raise awareness that in an interconnected world, pandemics, such as COVID-19, require a global approach. Motivated by the ongoing COVID-19 pandemic, we model here the spread of a virus in interconnected communities and explore different vaccination scenarios, assuming that the efficacy of the vaccination wanes over time. We start with susceptible populations and consider a susceptible–vaccinated–infected–recovered model with unvaccinated (“Bronze”), moderately vaccinated (“Silver”), and very-well-vaccinated (“Gold”) communities, connected through different types of networks via a diffusive linear coupling for local spreading. We show that when considering interactions in “Bronze”–“Gold” and “Bronze”–“Silver” communities, the “Bronze” community is driving an increase in infections in the “Silver” and “Gold” communities. This shows a detrimental, unidirectional effect of non-vaccinated to vaccinated communities. Regard...

$Research paper thumbnail of Solving fractional differential equation by an operational matrix of integration$

In this article we proposed an algorithm to obtain an approximation solution for fractional diffe... more In this article we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in Riemann-Liouville sense, based on shifted Legendre polynomials. This method has applied to solve linear multi-order fractional differential equation with initial conditions, and the exact solutions obtained for a illustrated examples.

$Research paper thumbnail of Existence of positive solutions for a class of fractional differential equation systems with multi-point boundary conditions$

Georgian Mathematical Journal, 2014

In this article, we study the existence of positive solutions of a multi-point boundary value pro... more In this article, we study the existence of positive solutions of a multi-point boundary value problem for some system of fractional differential equations. The fixed point theorem on cones will be applied to demonstrate the existence of solutions for this system. At the end, an example shows the application of the main results.

$Research paper thumbnail of Positive solutions for fractional differential equations with three-point multi-term fractional integral boundary conditions$

Advances in Difference Equations, 2014

We are concerned with the existence of at least one, two or three positive solutions for the boun... more We are concerned with the existence of at least one, two or three positive solutions for the boundary value problem with three-point multi-term fractional integral boundary conditions: D q u(t) + f (t, u(t)) = 0, 1 < q ≤ 2, 0 < t < 1, u(0) = 0, u(1) = m i=1 α i (I p i u)(η), 0 < η < 1, where D q is the standard Riemann-Liouville fractional derivative. Our analysis relies on the Krasnoselskii fixed point theorem and the Leggett-Williams fixed point theorem. Some examples are also given to illustrate the main results.

$Research paper thumbnail of Dynamical behaviours of Bazykin-Berezovskaya model with fractional-order and its discretization$

Computational Methods for Differential Equations, 2021

‎This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya... more ‎This paper is devoted to study dynamical behaviours of the fractional-order Bazykin-Berezovskaya model and its discretization‎. ‎The fractional derivative has been described in the Caputo sense‎. ‎We show that the discretized system‎, ‎exhibits more complicated dynamical behaviours than its corresponding fractional-order model‎. ‎Specially‎, ‎in the discretized model Neimark-Sacker and flip bifurcations and also chaos phenomena will happen‎. ‎In the final part‎, ‎some numerical simulation verify the analytical results‎.

International Journal of Nonlinear Analysis and Applications, 2016

In this article, we apply two new fixed point theorems to investigate the existence of mild solut... more In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.

In this paper, we study the monotonicity and convexity of the period function associated with cen... more In this paper, we study the monotonicity and convexity of the period function associated with centers of a specific class of symmetric Newtonian systems of degree 8. In this regard, we prove that if the period annulus surrounds only one elementary center, then the corresponding period function is monotone; but, for the other cases, the period function has exactly one critical point. We also prove that in all cases, the period function is convex.

In this article we have applied a numerical finite difference method to solve the Black-Scholes E... more In this article we have applied a numerical finite difference method to solve the Black-Scholes European and American option pricing both presented by fractional differential equations in time and asset.

Agronomy

This work investigates an experimental study for using low-cost and eco-friendly oils to increase... more This work investigates an experimental study for using low-cost and eco-friendly oils to increase the shelf life of strawberry fruit. Three natural oils were used: (i) Eucalyptus camaldulensis var obtuse, (ii) Mentha piperita green aerial parts essential oils (EOs), and (iii) Moringa oleifera seeds n-hexane fixed oil (FO). Furthermore, a mixture of EOs from E. camaldulensis var obtusa and M. piperita (1/1 v/v) was used. The treated fruits were stored at 5 °C and 90% relative humidity (RH) for 18 days. HPLC was used to analyse the changes in phenolic compounds during the storage periods. The effects of biofumigation through a slow-release diffuser of EOs (E. camaldulensis var obtusa and M. piperita), or by coating with M. oleifera FO, were evaluated in terms of control of post-harvest visual and chemical quality of strawberry fruits. The post-harvest resistance of strawberry fruits to Botrytis cinerea fungal infection was also evaluated. As a result, the EO treatments significantly r...

Journal of Mathematical Extension, 2021

In this paper, the dynamics of a modied Nicholson-Baileymodel as a discrete dynamical system has ... more In this paper, the dynamics of a modied Nicholson-Baileymodel as a discrete dynamical system has been studied. Local dynamics in a neighborhood of boundary xed points are investigated. Itis also proved that the model has a unique positive xed point and a Neimark-Sacker bifurcation emerges at this xed point. Some numericalsimulations are presented to illustrate the analytical results.