Ali Ahmadian

A Jacobi operational matrix for solving a fuzzy linear fractional differential equation

This paper reveals a computational method based using a tau method with Jacobi polynomials for the solution of fuzzy linear fractional differential equations of order 0<v<1. A suitable representation of the fuzzy solution via Jacobi polynomials diminishes its numerical results to the solution of a system of algebraic equations. The main advantage of this method is its high robustness and accuracy gained by a small number of Jacobi functions. The efficiency and applicability of the proposed method are proved by several test examples.PACS Codes:02, 02.30.Jr, 02.60.-x, 45.10.Hj.

Tau method for the numerical solution of a fuzzy fractional kinetic model and its application to the oil palm frond as a promising source of xylose

The Oil Palm Frond (a lignocellulosic material) is a high-yielding energy crop that can be utilized as a promising source of xylose. It holds the potential as a feedstock for bioethanol production due to being free and inexpensive in terms of collection, storage and cropping practices. The aim of the paper is to calculate the concentration and yield of xylose from the acid hydrolysis of the Oil Palm Frond through a fuzzy fractional kinetic model. The approximate solution of the derived fuzzy fractional model is achieved by using a tau method based on the fuzzy operational matrix of the generalized Laguerre polynomials. The results validate the effectiveness and applicability of the proposed solution method for solving this type of fuzzy kinetic model. A new fractional kinetic equation under uncertainty was addressed to depict the chemical reaction arising in Palm Oil Frond.An efficient numerical simulation based on a tau method was derived to solve the proposed kinetic equation.Different cases were solved to demonstrate the validity and efficiency of the proposed technique.

An Operational Matrix Based on Legendre Polynomials for Solving Fuzzy Fractional-Order Differential Equations

This paper deals with the numerical solutions of fuzzy fractional differential equations under Caputo-type fuzzy fractional derivatives of order . We derived the shifted Legendre operational matrix (LOM) of fuzzy fractional derivatives for the numerical solutions of fuzzy fractional differential equations (FFDEs). Our main purpose is to generalize the Legendre operational matrix to the fuzzy fractional calculus. The main characteristic behind this approach is that it reduces such problems to the degree of solving a system of algebraic equations which greatly simplifies the problem. Several illustrative examples are included to demonstrate the validity and applicability of the presented technique.

Application of Fuzzy Fractional Kinetic Equations to Modelling of the Acid Hydrolysis Reaction

In view of the usefulness and a great importance of the kinetic equation in specific chemical engineering problems, we discuss the numerical solution of a simple fuzzy fractional kinetic equation applied for the hemicelluloses hydrolysis reaction. The fuzzy approximate solution is derived based on the Legendre polynomials to the fuzzy fractional equation calculus. Moreover, the complete error analysis is explained based on the application of fuzzy Caputo fractional derivative. The main advantage of the present method is its superior accuracy which is obtained by using a limited number of Legendre polynomials. The method is computationally interesting, and the numerical results demonstrate the effectiveness and validity of the method for solving fuzzy fractional differential equations.

Solving differential equations of fractional order using an optimization technique based on training artificial neural network

The current study aims to approximate the solution of fractional differential equations (FDEs) by using the fundamental properties of artificial neural networks (ANNs) for function approximation. In the first step, we derive an approximate solution of fractional differential equation (FDE) by using ANNs. In the second step, an optimization approach is exploited to adjust the weights of ANNs such that the approximated solution satisfies the FDE. Different types of FDEs including linear and nonlinear terms are solved to illustrate the ability of the method. In addition, the present scheme is compared with the analytical solution and a number of existing numerical techniques to show the efficiency of ANNs with high accuracy, fast convergence and low use of memory for solving the FDEs.

An Eigenvalue-Eigenvector Method for Solving a System of Fractional Differential Equations with Uncertainty

A new method is proposed for solving systems of fuzzy fractional differential equations (SFFDEs) with fuzzy initial conditions involving fuzzy Caputo differentiability. For this purpose, three cases are introduced based on the eigenvalue-eigenvector approach; then it is shown that the solution of system of fuzzy fractional differential equations is vector of fuzzy-valued functions. Then the method is validated by solving several examples.

Effects of the surface modification of carbon fiber by growing different types of carbon nanomaterials on the mechanical and thermal properties of polypropylene

The potential usage of different types of carbon nanoparticles in the herringbone, tubular and sheet structures of graphene plates, such as carbon nanofibers (CNF), carbon nanotubes (CNT) and graphene (G) flakes and also CNF–G and CNT–G on the carbon fiber (CF) surface as fillers in composite materials, is discussed in this paper. The combination of 2D graphene of high charge density and 1D CNTs or CNFs of large surface areas generates a versatile 3D hybrid network with synergic properties. A one-step process, chemical vapour deposition technique has been applied to synthesis these carbon nanoparticles (1D, 2D and 3D structures) by use of bimetallic catalyst (Ni/Cu). The morphology and chemical structure of the fibers, which have an effect on the polymer properties, were characterized by means of scanning electron microscopy, transmission electron microscopy, and specially Raman spectroscopy. These techniques were used to identify carbon nanoparticles, access their dispersion in polymers, evaluate filler/matrix interactions and detect polymer phase transitions. Compared with the neat CFs, the synthesized hybrid fibers led to an increase of the BET surface area from 0.7 m2 g−1 to 46 m2 g−1. Besides that, polypropylene (PP) composites with different carbon-based fillers, such as G on CF (CF–G), CNF on CF (CF–CNF), CNT on CF (CF–CNT) and also CF–CNF–G and CF–CNT–G were prepared by the melt mixed method, and the effects of these particles on the mechanical and thermal properties were analyzed. The mechanical results were confirmed by a mathematical model that state the mechanical reinforcement of the resultant composites strongly depends on the type of filler used. Noteworthy, composites based on combination of G and CNT presented the highest mechanical and thermal properties than those based on other carbon nanoparticles.

Effect of growing graphene flakes on branched carbon nanofibers based on carbon fiber on mechanical and thermal properties of polypropylene

A one-step process, the chemical vapor deposition method, has been used to fabricate graphene flakes (G) on branched carbon nanofibers (CNF) grown on carbon fibers (CF). In this contribution, the G–CNF–CF fibers have been used as reinforcing fillers in a polypropylene (PP) matrix in order to improve the mechanical and thermal properties of the PP. A bimetallic catalyst (Ni/Cu) was deposited on a CF surface to synthesize branched CNF using C2H2/H2 precursors at 600 °C followed by growing G flakes at 1050 °C. The morphology and chemical structure of the G–CNF–CF fibers were characterized by means of electron microscopy, transmission electron microscopy, and Raman spectroscopy. The mechanical and thermal behaviors of the synthesized G–CNF–CF/PP composite were characterized by means of tensile tests and thermal gravimetric analysis. Mechanical measurements revealed that the tensile stress and Youngs modulus of the G–CNF–CF/PP composites were higher than the neat PP with the contribution of 76%, 73%, respectively. Also, the thermal stability of the resultant composite increased about 100 °C. The measured reinforcement properties of the fibers were fitted with a mathematical model obtaining good agreement between the experimental results and analytical solutions.

A New fractional derivative for differential equation of fractional order under interval uncertainty

In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models.

Numerical Solution of Second-Order Fuzzy Differential Equation Using Improved Runge-Kutta Nystrom Method

We develop the Fuzzy Improved Runge-Kutta Nystrom (FIRKN) method for solving second-order fuzzy differential equations (FDEs) based on the generalized concept of higher-order fuzzy differentiability. The scheme is two-step in nature and requires less number of stages which leads to less number of function evaluations in comparison with the existing Fuzzy Runge-Kutta Nystrom method. Therefore, the new method has a lower computational cost which effects the time consumption. We assume that the fuzzy function and its derivative are Hukuhara differentiable. FIRKN methods of orders three, four, and five are derived with two, three, and four stages, respectively. The numerical examples are given to illustrate the efficiency of the methods.