Efficient schemes on solving fractional integro-differential equations

Fractional integro-differential equation (FIDE) emerges in various modelling of physical phenomena. In most cases, finding the exact analytical solution for FIDE is difficult or not possible. Hence, the methods producing highly accurate numerical solution in efficient ways are often sought after. This research has designed some methods to find the approximate solution of FIDE. The analytical expression of Genocchi polynomial operational matrix for left-sided and right-sided Caputo’s derivative and kernel matrix has been derived. Linear independence of Genocchi polynomials has been proved by deriving the expression for Genocchi polynomial Gram determinant. Genocchi polynomial method with collocation has been introduced and applied in solving both linear and system of linear FIDE. The numerical results of solving linear FIDE by Genocchi polynomial are compared with certain existing methods. The analytical expression of Bernoulli polynomial operational matrix of right-sided Caputo’s fractional derivative and the Bernoulli expansion coefficient for a two-variable function is derived. Linear FIDE with mixed left and right-sided Caputo’s derivative is first considered and solved by applying the Bernoulli polynomial with spectral-tau method. Numerical results obtained show that the method proposed achieves very high accuracy. The upper bounds for th

Child\u27s play the developmental benefits of the play choices of modern children: Implications for school curricula

This paper presents data from the Irish Neighbourhood Play Study. The Irish Neighbourhood Play Study explored the play choices of children from 0 to 15 years of age. This paper reports the findings on the play choices of children and these are presented alongside the levels of engagement within each play type. Construction Play, Motor Play, Fantasy (Imaginative) Play and Social Play are all applied as broad categories with detailed data presented that drills down into what elements of play children are choosing within each category. The developmental benefits of each play type are then explored and discussed. These findings are viewed through an educational lens and contextualised within a curricular context. The critical questions arising from the findings concern the developmental benefits inherent to the types of play children choose for themselves and how these developmental benefits translate to the school context. This paper discusses these critical questions and suggests possible implications for school curricula when adopting play-based approaches

An intelligent recommendation system framework for student relationship management

In order to enhance student satisfaction, many services have been provided in order to meet student needs. A recommendation system is a significant service which can be used to assist students in several ways. This paper proposes a conceptual framework of an Intelligent Recommendation System in order to support Student Relationship Management (SRM) for a Thai private university. This article proposed the system architecture of an Intelligent Recommendation System (IRS) which aims to assist students to choose an appropriate course for their studies. Moreover, this study intends to compare different data mining techniques in various recommendation systems and to determine appropriate algorithms for the proposed electronic Intelligent Recommendation System (IRS). The IRS also aims to support Student Relationship Management (SRM) in the university. The IRS has been designed using data mining and artificial intelligent techniques such as clustering, association rule and classification