the current paper contributes a novel framework for solving a class of linear matrix differential equations. to do so, the operational matrix of the derivative based on the shifted bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. an error estimation of presented method is provided. numerical experiments are...

enamel matrix derivative emdogain (emd) is widely used in periodontal treatment in spite of the fact that its effect on the developing embryo has not been elucidated. the aim of this study was to investigate the teratogenic effect of emd on the rat embryo neural crest cells. the neural crest is a unique population of cells that migrates from the dorsal neural tube along defined pathways and pro...

objective: the aim of this study was to compare subepithelial connective tissue grafts (sctg) and coronally advanced flaps (caf) with the addition of emdogain in the treatment of gingival recession. materials and methods : this interventional randomized controlled clinical trial involved eleven patients and 31 teeth demonstrating facial recessions of > 2 mm identified as miller's class i or ii....

background: the aim of this clinical trial study was to clinically evaluate the use of enamel matrix protein derivative combined with the coronally positioned fl ap to treat gingival recession compared to the subepithelial connective tissue graft by a new method to obtain denuded root surface area. materials and methods: thirteen patients, each with two or more similar bilateral miller class i ...

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

In this paper we introduce a type of fractional-order polynomials based on the classical Chebyshev polynomials of the second kind (FCSs). Also we construct the operational matrix of fractional derivative of order $ gamma $ in the Caputo for FCSs and show that this matrix with the Tau method are utilized to reduce the solution of some fractional-order differential equations.

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

in this manuscript a new method is introduced for solving fractional differential equations. the fractional derivative is described in the caputo sense. the main idea is to use fractional-order legendre wavelets and operational matrix of fractional-order integration. first the fractional-order legendre wavelets (flws) are presented. then a family of piecewise functions is proposed, based on whi...

In this paper‎, ‎first‎, ‎a numerical method is presented for solving a class of linear Fredholm integro-differential equation‎. ‎The operational matrix of derivative is obtained by introducing hybrid third kind Chebyshev polynomials and Block-pulse functions‎. ‎The application of the proposed operational matrix with tau method is then utilized to transform the integro-differential equations to...