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Institute for Advanced Studies in Basic Sciences (IASBS)

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Home>Department of Mathematics>
Department of Mathematics
 
 
Alireza Khastan  
Assistant Professor
Room: Mathematics Building 113
Tel: 33155113
Fax: 33155097
Email:
Personal Homepage

Research interests:

Numerical Analysis, Fuzzy Differential Equations.


Research area:

Numerical Analysis, Fuzzy Differential Equations


Publications:
Journal
1- Khastan, A., "A new representation for inverse fuzzy transform and its application", Soft Computing, 1-10, (2017).

Abstract:
In this study, a new representation formula for basic functions of fuzzy transform is introduced and some new approximating properties of the inverse fuzzy transform are described. In particular, using block pulse functions, we present properties of sinusoidal basic functions. As an application, we present a new fuzzy-based method for numerical solution of nonlinear Fredholm integral equations.
2- Khastan, A., "FUZZY LOGISTIC DIFFERENCE EQUATION", Iranian Journal of Fuzzy Systems (IJFS), 14: (2), 47-58, (2017).

Abstract:
In this study, we consider two different inequivalent formulations of the logistic difference equation $x_{n+1}= eta x_n(1- x_n), n=0,1,..., $ where $x_n$ is a sequence of fuzzy numbers and $eta$ is a positive fuzzy number. The major contribution of this paper is to study the existence, uniqueness and global behavior of the solutions for two corresponding equations, using the concept of Hukuhara difference for fuzzy numbers. Finally, some examples are given to illustrate our results.
3- Khastan, A., Rodriguez-Lopez, R., "On the solutions to first order linear fuzzy differential equations", Fuzzy Sets and Systems, 295, 114-135, (2016).

Abstract:
In this paper, we study different formulations of first order linear fuzzy differential equations using the concept of generalized differentiability. We present sufficient conditions for the existence of solutions and obtain the general expression of these solutions, which exhibit different behavior. Some examples are given to illustrate our results.
4- Amrahov, S. E., Khastan, A., Gasilov, N., Fatullayev, A. G., "Relationship between Bede–Gal differentiable set-valued functions and their associated support functions", Fuzzy Sets Syst., 295, 57-71, (2016).

Abstract:
In this study, we adapt the concept of the Bede–Gal derivative, which was initially suggested for fuzzy number-valued functions, to set-valued functions. We use an example to demonstrate that this concept overcomes some of the shortcomings of the Hukuhara derivative. We prove some properties of Bede–Gal differentiable set-valued functions. We also study the relationship between a Bede–Gal differentiable set-valued function and its value's support function, which we call the associated support function. We provide examples of set-valued functions that are not Bede–Gal differentiable whereas their associated support functions are differentiable. We also present some applications of the Bede–Gal derivative to solving set-valued differential equations.
5- Khastan, A., Rodríguez-López, R., "On the solutions to first order linear fuzzy differential equations", Fuzzy Sets and Systems, 295, 114-135, (2016).

Abstract:
In this paper, we study different formulations of first order linear fuzzy differential equations using the concept of generalized differentiability. We present sufficient conditions for the existence of solutions and obtain the general expression of these solutions, which exhibit different behavior. Some examples are given to illustrate our results
Conferences
1- Khastan, A., "Solution of First Order Linear Difference Equations with Uncertainty", The International Conference Mathematical and Computational Modeling in Science and Technology,Izmir-Turkey(August 02-07,2015): (10), 37-, (2015).

Abstract:
We study the different formulations of first order linear difference equations with uncer- tain initial value. We obtain the explicit expressions of the solutions for three in-equivalent difference equations while they are equivalent in the classical case
2- Chalco-Cano, Y., Khastan, A., Rodriguez-Lopez, R., "Normalized expression for solutions to linear fuzzy differential equations under combination of differences", 16th World Congress of the International Fuzzy Systems Association (IFSA) 9th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), 1382-1388, (2015).

Abstract:
We give a normalized expression for the solutions to the initial value problem for some linear fuzzyinterval differential equations by using a general notation which allows the combination of two types of differences. By switching between these types of differences, we derive several expressions for solutions corresponding to strongly generalized differentiability, providing a general formulation for these solutions to linear problems.
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