University of Kashan

About: University of Kashan is a education organization based out in Kāshān, Iran. It is known for research contribution in the topics: Catalysis & Nanocomposite. The organization has 3034 authors who have published 6965 publications receiving 116317 citations.

A new operational matrix for solving fractional-order differential equations

Abstract: 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. This paper deals with the numerical solution of a class of fractional differential equations. The fractional derivatives are described in the Caputo sense. Our main aim is to generalize the Legendre operational matrix to the fractional calculus. In this approach, a truncated Legendre series together with the Legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.

A Review on Chitin and Chitosan Polymers: Structure, Chemistry, Solubility, Derivatives, and Applications

Abstract: Chitin and chitosan are considerably versatile and promising biomaterials. The deacetylated chitin derivative chitosan is a useful and interesting bioactive polymer. Despite its biodegradability, it has many reactive amino side groups, which offer possibilities of chemical modifications, formation of a large variety of beneficial derivatives, which are commercially available or can be made available via graft reactions and ionic interactions. This study looks at the contemporary research in chitin and chitosan towards structure, properties, and applications in various industrial and biomedical fields.

Solving nonlinear fractional partial differential equations using the homotopy analysis method

Abstract: In this article, the homotopy analysis method is applied to solve nonlinear fractional partial differential equations. On the basis of the homotopy analysis method, a scheme is developed to obtain the approximate solution of the fractional KdV, K(2,2), Burgers, BBM-Burgers, cubic Boussinesq, coupled KdV, and Boussinesq-like B(m,n) equations with initial conditions, which are introduced by replacing some integer-order time derivatives by fractional derivatives. The homotopy analysis method for partial differential equations of integer-order is directly extended to derive explicit and numerical solutions of the fractional partial differential equations. The solutions of the studied models are calculated in the form of convergent series with easily computable components. The results of applying this procedure to the studied cases show the high accuracy and efficiency of the new technique. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010