Bibliografische Information der Deutschen NationalbibliothekDie Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.de abrufbar. Universitätsverlag AbstractThis paper examines and develops matrix methods to approximate the eigenvalues of a fourth order Sturm-Liouville problem subjected to a kind of fixed boundary conditions, furthermore, it extends the matrix methods for a kind of general boundary conditions. The idea of the methods comes from finite difference and Numerov's method as well as boundary value methods for second order regular Sturm-Liouville problems. Moreover, the determination of the correction term formulas of the matrix methods are investigated in order to obtain better approximations of the problem with fixed boundary conditions since the exact eigenvalues for q = 0 are known in this case. Finally, some numerical examples are illustrated.

Summary In this paper, an efficient and accurate computational method based on the hybrid of block‐pulse functions and Taylor polynomials is proposed for solving a class of fractional optimal control problems. In the proposed method, the Riemann‐Liouville fractional integral operator for the hybrid of block‐pulse functions and Taylor polynomials is given. By taking into account the property of this operator, the solution of fractional optimal control problems under consideration is reduced to a nonlinear programming one to which existing well‐developed algorithms may be applied. The present method applies to both fractional optimal control problems with or without inequality constraints. The method is computationally very attractive and gives very accurate results. Easy implementation and simple operations are the essential features of the proposed hybrid functions. Illustrative examples are given to assess the effectiveness of the developed approximation technique.

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This paper includes the notions of neutrosophic n-ary N-subgroupoids of n-ary groupoids  and some properties.