Soheil Salahshour | Bahcesehir University (original) (raw)

Papers by Soheil Salahshour

Journal of Computational and Applied Mathematics, Jun 1, 2011

In this paper, we shall propose a new method to obtain symmetric solutions of a fully fuzzy linea... more In this paper, we shall propose a new method to obtain symmetric solutions of a fully fuzzy linear system (FFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a FFLS (in the present paper, we assumed that the 1-cut of a FFLS is a crisp linear system or equivalently, the matrix coefficient and right hand side have triangular shapes), then some unknown symmetric spreads are allocated to each row of a 1-cut of a FFLS. So, after some manipulations, the original FFLS is transformed to solving 2n linear equations to find the symmetric spreads. However, our method always give us a fuzzy number vector solution. Moreover, using the proposed method leads to determining the maximal-and minimal symmetric solutions of the FFLS which are placed in a Tolerable Solution Set and a Controllable Solution Set, respectively. However, the obtained solutions could be interpreted as bounded symmetric solutions of the FFLS which are useful for a large number of multiplications existing between two fuzzy numbers. Finally, some numerical examples are given to illustrate the ability of the proposed method.

$Research paper thumbnail of Existence and uniqueness results for fractional differential equations with uncertainty$

Advances in Difference Equations, Jul 19, 2012

In this paper, we study the existence, uniqueness and approximate solutions of fuzzy fractional d... more In this paper, we study the existence, uniqueness and approximate solutions of fuzzy fractional differential equations (FFDEs) under Caputo's H-differentiability. To this end, the concept of Riemann-Liouville's H-differentiability is introduced, and subsequently, the Caputo's H-differentiability is proposed. Moreover, the related fuzzy Volterra integral forms of FFDEs are obtained which are applied to construct two converge consequences of fuzzy-valued functions as approximated solutions of FFDEs.

$Research paper thumbnail of Extension of the fractional derivative operator of the Riemann-Liouville$

The Journal of Nonlinear Sciences and Applications, Jun 5, 2017

By using the generalized beta function, we extend the fractional derivative operator of the Riema... more By using the generalized beta function, we extend the fractional derivative operator of the Riemann-Liouville and discusses its properties. Moreover, we establish some relations to extended special functions of two and three variables via generating functions.

$Research paper thumbnail of Solving fuzzy fractional differential equations by fuzzy Laplace transforms$

Communications in Nonlinear Science and Numerical Simulation, Mar 1, 2012

This paper deals with the solutions of fuzzy fractional differential equations (FFDEs) under Riem... more This paper deals with the solutions of fuzzy fractional differential equations (FFDEs) under Riemann–Liouville H-differentiability by fuzzy Laplace transforms. In order to solve FFDEs, it is necessary to know the fuzzy Laplace transform of the Riemann–Liouville H-derivative of f,[Formula: see text]. The virtue of [Formula: see text] is that can be written in terms of L [f (x)]. Moreover, some illustrative examples are solved to show the efficiency and utility of Laplace transforms method.

Procedia Computer Science, 2011

Linear systems have important applications in many branches of science and engineering in many ap... more Linear systems have important applications in many branches of science and engineering in many applications, at least some of the parameters of the system are represented by fuzzy rather than crisp numbers. So, it is immensely important to develop a numerical procedure that would appropriately treat general fuzzy linear systems and solve them. In this paper, we propose bounded and symmetric solutions of fully fuzzy linear systems in the dual form (DFFLS) based on a 1-cut expansion. To this end, we solve the 1-cut of a DFFLS (we assumed that the 1-cut of a DFFLS is a crisp linear system), then some unknown symmetric spreads are allocated to each row of a 1-cut of a DFFLS. So, after some manipulations, the original DFFLS is transformed to solving 2* n linear equations to find the symmetric spreads. However, our method always give us a fuzzy vector solution. Moreover, we show that the bounded and symmetric solution of the DFFLS will be placed in the tolerable solution set (TSS) and in the controllable solution set (CSS), respectively. Also, an economic example is solved to illustrate the ability of proposed method and a new pattern is suggested for comparing the obtained solutions.

$Research paper thumbnail of Improved reproducing kernel method to solve space-time fractional advection-dispersion equation$

In this paper, we consider the Space-Time Fractional Advection-Dispersion equation on a finite do... more In this paper, we consider the Space-Time Fractional Advection-Dispersion equation on a finite domain with variable coefficients. Fractional Advection-Dispersion equation as a model for transporting heterogeneous subsurface media as one approach to the modeling of the generally non-Fickian behavior of transport. We use a semi-analytical method as Reproducing kernel Method to solve the Space-Time Fractional Advection-Dispersion equation so that we can get better approximate solutions than the

$Research paper thumbnail of A fuzzy method for solving fuzzy fractional differential equations based on the generalized fuzzy Taylor expansion$

Authorea (Authorea), Jul 26, 2020

In many mathematical types of research, in order to solve the fuzzy fractional differential equat... more In many mathematical types of research, in order to solve the fuzzy fractional differential equations, we should transform these problems into crisp corresponding problems and by solving them the approximate solution can be obtained. The aim of this paper is to present a new direct method to solve the fuzzy fractional differential equations without this transformation. In this work, the fuzzy generalized Taylor expansion by using the sense of fuzzy Caputo fractional derivative for fuzzy-valued functions is presented. For solving fuzzy fractional differential equations, the fuzzy generalized Euler's method is applied. In order to show the accuracy and efficiency of the presented method, the local and global truncation errors are determined. Moreover, the consistency, the convergence and the stability of the generalized Euler's method are proved in detail. Eventually, the numerical examples, especially in the switching point case, show the flexibility and the capability of the presented method.

$Research paper thumbnail of Retraction Note: Fuzzy fractional Ostrowski inequality with Caputo differentiability$

Journal of Inequalities and Applications, Aug 30, 2013

Springer eBooks, Jul 26, 2021

$Research paper thumbnail of RETRACTED ARTICLE: Fuzzy fractional Ostrowski inequality with Caputo differentiability$

Journal of Inequalities and Applications, Feb 14, 2013

The use of fractional inequalities in mathematical models is increasingly widespread in recent ye... more The use of fractional inequalities in mathematical models is increasingly widespread in recent years. In this manuscript, we firstly propose the right Caputo derivative of fuzzy-valued functions about fractional order ν (0 < ν < 1). To this end, we consider two types of differentiability (similar to the non-fractional case). Then we derive the equivalent integral forms of original fuzzy fractional differential equations. Finally, we prove the fuzzy Ostrowski inequality involving three functions under Caputo's differentiability. In this regard, we state some new results.

$Research paper thumbnail of RETRACTED: On the fractional Ostrowski inequality with uncertainty$

Journal of Mathematical Analysis and Applications, Nov 1, 2012

In this paper, we first propose the right and the left fuzzy Riemann-Liouville integrals; then th... more In this paper, we first propose the right and the left fuzzy Riemann-Liouville integrals; then the related left and right fuzzy Caputo differentiabilities are introduced. Consequently, some useful results about integration and differentiation of fractional order under uncertainty have been obtained. Moreover, some equivalent integral forms of original fuzzy fractional differential equations are derived. Finally, the fuzzy Ostrowski inequality about fractional case has been stated.

$Research paper thumbnail of A comment on “Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations”$

Communications in Nonlinear Science and Numerical Simulation, May 1, 2014

In a recent paper [R. Alikhani, F. Bahrami, Global solutions for nonlinear fuzzy fractional integ... more In a recent paper [R. Alikhani, F. Bahrami, Global solutions for nonlinear fuzzy fractional integral and integrodifferential equations, Communications in Nonlinear Science and Numerical Simulation, In press], we found some defects about the exact solutions of given examples. Also, the main result (Theorem 4.5) is not fulfilled. For this purpose, some examples are given.

Abstract and Applied Analysis, 2013

We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-call... more We propose a method to approximate the solutions of fully fuzzy linear system (FFLS), the so-called general solutions. So, we firstly solve the 1-cut position of a system, then some unknown spreads are allocated to each row of an FFLS. Using this methodology, we obtain some general solutions which are placed in the well-known solution sets like Tolerable solution set (TSS) and Controllable solution set (CSS). Finally, we solved two examples in order to demonstrate the ability of the proposed method.

Soft Computing, Oct 1, 2010

In this paper, we study the numerical method for solving hybrid fuzzy differential using Euler me... more In this paper, we study the numerical method for solving hybrid fuzzy differential using Euler method under generalized Hukuhara differentiability. To this end, we determine the Euler method for both cases of H-differentiability. Also, the convergence of the proposed method is studied and the characteristic theorem is given for both cases. Finally, some numerical examples are given to illustrate the efficiency of the proposed method under generalized Hukuhara differentiability instead of suing Hukuhara differentiability.

$Research paper thumbnail of M-fractional derivative under interval uncertainty: Theory, properties and applications$

Chaos Solitons & Fractals, Dec 1, 2018

In the recent years some efforts were made to propose simple and well-behaved fractional derivati... more In the recent years some efforts were made to propose simple and well-behaved fractional derivatives that inherit the classical properties from the first order derivative. In this regards, the truncated M-fractional derivative for α-differentiable function was recently introduced that is a generalization of four fractional derivatives presented in the literature and has their important features. In this research, we aim to generalize this novel and effective derivative under interval uncertainty. The concept of interval truncated M-fractional derivative is introduced and some of the distinguished properties of this interesting fractional derivative such as Rolle's and mean value theorems, are developed for the interval functions. In addition, the existence and uniqueness conditions of the solution for the interval fractional differential equations (IFDEs) based on this new derivative are also investigated. Finally, we present the applicability of this novel interval fractional derivative for IFDEs based on the notion of w-increasing (w-decreasing) by solving a number of test problems.

Soft Computing, Aug 12, 2012

Abstract A natural way to model dynamic systems under uncertainty is to use fuzzy initial value p... more Abstract A natural way to model dynamic systems under uncertainty is to use fuzzy initial value problems (FIVPs) and related uncertain systems. In this paper, we express the fuzzy Laplace transform and then some of its well-known properties are investigated. In addition, an existence theorem is given for fuzzy-valued function which possess the fuzzy Laplace transform. Consequently, we investigate the solutions of FIVPs and the solutions in state-space description of fuzzy linear continuous-time systems under generalized H- ...

Entropy, Feb 16, 2015

In this paper, we apply the concept of Caputo's H-differentiability, constructed based on the gen... more In this paper, we apply the concept of Caputo's H-differentiability, constructed based on the generalized Hukuhara difference, to solve the fuzzy fractional differential equation (FFDE) with uncertainty. This is in contrast to conventional solutions that either require a quantity of fractional derivatives of unknown solution at the initial point (Riemann-Liouville) or a solution with increasing length of their support (Hukuhara difference). Then, in order to solve the FFDE analytically, we introduce the fuzzy Laplace transform of the Caputo H-derivative. To the best of our knowledge, there is limited research devoted to the analytical methods to solve the FFDE under the fuzzy Caputo fractional differentiability. An analytical solution is presented to confirm the capability of the proposed method.

The Scientific World Journal, 2014

In recent years, a remarkably large number of inequalities involving the fractional-integral oper... more In recent years, a remarkably large number of inequalities involving the fractional-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractional-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kober type fractional-integral operators. The cases of synchronous functions as well as of functions bounded by integrable functions are considered.

$Research paper thumbnail of On the fractional Ostrowski inequality with uncertainty$

In this paper, we first propose the right and the left fuzzy Riemann–Liouville integrals; then th... more In this paper, we first propose the right and the left fuzzy Riemann–Liouville integrals; then the related left and right fuzzy Caputo differentiabilities are introduced. Consequently, some useful results about integration and differentiation of fractional order under uncertainty have been obtained. Moreover, some equivalent integral forms of original fuzzy fractional differential equations are derived. Finally, the fuzzy Ostrowski inequality about fractional case has been stated.