Safar Irandoust-pakchin

• Associate Professor, Ph. D
• Professor (Associate) at University of Tabriz

In this article, time-fractional advection-dispersion equation is considered. Fractional derivative is in the Caputo sense and for approximating the first and second derivatives, the modified generalized Laguerre polynomials (MGLPs) have been used. The MGLPs (L^{α,β}_n(x)) have two parameter α > −1 and β > 0. These polynomials, orthogonal polynomia...

In this manuscript, we study and examine the time‐fractional modified anomalous sub‐diffusion model of distributed‐order. Two numerical approaches are used to study the approximate solutions of the presented model. For the first approach, we use a second‐order difference method based on the L1 formula for the temporal variable. In this case, stabil...

This paper presents a groundbreaking method for solving the multi–order fractional differential (M-OFD), both linear and nonlinear, as well as fractional partial differential equations (FPDE)s. This approach involves constructing an operational matrix of fractional derivatives using linear B-spline (LB-S) wavelet functions with perfect subtlety.The...

This study introduces a new numerical approach named flatlet oblique multiwavelets (FOMW) to solve fractional‐order stochastic integro‐differential equation (FSI‐DE). The FOMW is used to create an operational matrix of the stochastic integral, which helps transform the FSI‐DE into a linear system of algebraic equations. This method requires only a...

In this paper, a class of finite difference method (FDM) is designed for solving the time-fractional Liouville-Caputo and space-Riesz fractional diffusion equation. For this purpose, the fractional linear barycentric rational interpolation method (FLBRI) is adopted to discretize the Liouville-Caputo derivative in the time direction as well as the s...

In this paper, the time-fractional heat equation with the Caputo derivative of order α where 0 < α ≤ 1 is considered. The parametric Crank-Nicholson type method for direct problems is used. But for the inverse problem, for finding the best conduction parameter c and the best order of fractional derivative α, we use genetic algorithm (GA) for minimiz...

In this paper, a kind of the differential equation including a time–fractional sub–diffusion equation is considered. Through this memorandum, a well-known technique, in the time direction is adopted by the p-fractional linear multistep method (p-FLMM) according to the q-fractional backward difference formula (q-FBDF) of implicit type for q = 1, 2, 3,...

The main purpose of this paper is to numerically solve the fractional differential equations (FDE)s with the fractional order in (1, 2) using the implicit forms of the special case of fractional second linear multistep methods (FSLMM)s. The studies are focused on the stability properties and proving that the proposed methods are A(α)−stable. For thi...

One of the first characteristics of a damaged structure is a change in the local stiffness of the structure and the consequent change in its natural frequencies. In recent years, Compressive Sensing (CS) has achieved remarkable success compared to the Nyqu ist sampling rate. Compressive Sensing is based on the fact that most natural signals are spa...

In this paper, the explicit forms of the fractional second linear multistep methods (FSLMMs)are introduced for solving fractional differential equations (FDEs) of the fractional order in (1, 2). These explicit FSLMMs are constructed based on fractional backward difference formulas 1, 2, and 3 (FBDF1, FBDF2, and FBDF3) with the first, second, third, an...

This international seminar will be held on 13-14 July 2022 at the University of Tabriz. Main Covers: Differential Equations Dynamical Systems Application in (Image Processing, Medicine, Financial Mathematics, ...) Fractional Calculus (Theory and Applications) http://16diffdyn.ir/fa/

In this paper, the Black-Scholes (B-S) equation to price American options is studied which is governed by a partial differential problem. A nonlinear partial differential equation (PDE) is resulted by applying a penalty approach for this problem. To numerically solve this PDE, an equipped finite difference method with variable step size (VSS) in th...

The main aim of this paper is to develop a class of high-order finite difference method for the numerical solution of Caputo type time–fractional sub–diffusion equation. In the time direction, the Caputo derivative is discretized by employing a numerical technique based on the fractional linear barycentric rational interpolation method (FLBRI). The...

The main purpose of this paper is to develop a new method based on operational matrices of the linear cardinal B-spline (LCB-S) functions to numerically solve of the fractional stochastic integro-differential (FSI-D) equations. To reach this aim, LCB-S functions are introduced and their properties are considered, briefly. Then, the operational matr...

In this paper a novel image enhancement model based on shock filter for image deblurring is proposed in three cases. For the weight of shock filter, the fractional order derivative of initial blurry image is used. This fractional order weight can be adjusted adaptively according to the gradient of blurred image. Compared with the traditional intege...

In this paper, the Black–Scholes (B–S) model for the pricing of the European and the barrier call options are considered, which yields a partial differential problem. First, A numerical technique based on Crank–Nicolson (C–N) method is used to discreti- size the time domain. Consequently, the partial differential equation will be converted to a sys...

In this paper, a new generating function based on linear barycentric rational interpolation is introduced for the numerical solution of fractional differential equations which is designed on fractional linear multistep methods. The consistency of the proposed method is analyzed. considering monotonicity of the coefficients, the stability of the pro...

In this paper, beside studying in fields of electronic, image processing, computer vision, face recognition, filtering, wavelet transform, linear discriminant analysis and support vector machine, a new method for face recognition has been proposed. First, feature vectors are obtained from raw face images using Gabor wavelets. Next, the extracted...

This paper presents a novel and uniform algorithm for edge detection based on SVM (support vector machine) with Three-dimensional Gaussian radial basis function with kernel. Because of disadvantages in traditional edge detection such as inaccurate edge location, rough edge and careless on detect soft edge. The experimental results indicate how the...

In this paper, a variable-order fractional derivative nonlinear cable equation is considered. It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This pape...

In this paper, we first introduce a new homotopy perturbation method for solving a fractional order nonlinear cable equation. By applying proposed method the nonlinear equation it is changed to linear equation for per iteration of homotopy perturbation method. Then, we solve obtained problems with separation method. In examples, we illustrate that...

This paper presents a novel and uniform algorithm for edge detection based on SVM (support vector machine) with Three-dimensional Gaussian radial basis function with kernel. Because of disadvantages in traditional edge detection such as inaccurate edge location, rough edge and careless on detect soft edge. The experimental results indicate how the...

It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solu- tion of a class of fractional differential equation. The frac...

In this paper, we apply homotopy analysis method (HAM) for computing the eigenvalues of Sturm-Liouville problems. The parameter h, in this method, helps us to adjust and control the convergence region. The results show that this method has validity and high accuracy with less iteration number in compare to Variation Iteration Method (VIM) and Adomi...

In this paper, we first introduce a new homotopy perturbation method for solving a fractional order nonlinear cable equation. By applying proposed method the nonlinear equation it is changed to linear equation for per iteration of homotopy perturbation method. Then, we solve obtained problems with separation method. In examples, we illustrate that...

In this paper, first a new homotopy perturbation method for solving a fractional order nonlinear telegraph equation is introduced. By applying the proposed method, the nonlinear equation is translated to linear equations for per iteration of homotopy perturbation method. Then, the obtained problems are solved with separation method. In the examples...

In this paper, the modification of He's variational iteration method (MVIM) is developed to solve fractional integro-differential equations with nonlocal boundary conditions. It is shown that by choosing suitable initial approximation, the exact solution obtains by one iteration. It is illustrated that the propose method is effective and has high c...

In this paper we consider boundary value problems with singularity in equation or solution. To solve these problems, we apply single exponential and double exponential transformations of sinc-Galerkin and Chebyshev cardinal functions. Numerical examples highlight efficiency of Chebyshev cardinal functions and sinc-Galerkin method in problems with s...

In this paper, we introduce a modification of He’s variational iteration, homotopy analysis and optimal homotopy analysis methods for solving fractional boundary value problems. It is illustrated that the proposed methods are powerful fast numerical tools to find accurate solutions. It is illustrated that efficiency of these methods is based on pro...

In this paper we use homotopy Pad´e method for solving Painlv´e equation of type 1. The ability of this method in overcoming on the singular points difficulty, makes it to be efficient method in deal with Painlv´e equation.

A computational method for numerical solution of a nonlinear Volterra and Fredholm integro-differential equations of fractional order based on Chebyshev cardinal functions is introduced. The Chebyshev cardinal operational matrix of fractional derivative is derived and used to transform the main equation to a system of algebraic equations. Some exam...

This paper is concerned with the construction of biorthogonal multiwavelet basis in the unit interval to form a biorthogonal flatlet multiwavelet system. Next a method to calculate integer and fractional derivatives of the dual flatlet multiwavelets by multiplying some matrices is suggested. The system is then used to solve a fractional convection–...

In this paper, the homotopy analysis method (HAM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort harvesting. Numerical comparisons with the homotopy perturbation method (HPM), the Adomian decomposition method (ADM) and the RungeKutta (RK78) methods are presented. The HAM solutions contain th...

A numerical technique is presented for the solution of Fokker- Planck equation. This method uses the the flatlet oblique multiwavelets. The method consists of expanding the required approximate solution as the elements of the flatlet oblique multiwavelets scaling and wavelet bases. Using the operational matrix of derivative, we reduce the problem t...

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the...

In this paper, we apply the homotopy analysis method (HAM) to obtain approximate solution for the Ratio-dependent predator-prey system with constant effort harvesting. We optimize the values of h1 and h2 by an Euclidean residual for the system of equations. The validity of this method is verified, because it agrees with Runge-Kutta (RKF78) in figur...

In this paper, the modification of He's variational iteration method(MVIM) is developed to solve fractional ordinary differentialequations and fractional partial differential equations. It is usedthe free choice of initial approximation to propose the reliablemodification of He's variational iteration method. Some of thefractional differential equa...

In this paper, we apply the homotopy analysis method (HAM) to obtain approximate solution for the Ratio-dependent predator-prey system with constant effort harvesting. We optimize the values of h 1 and h 2 by an Euclidean residual for the system of equations. The validity of this method is verified, because it agrees with Runge-Kutta (RKF78) in fig...