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Differential superordinations defined by an integral operator

100%

Balaeti C. M.

Journal of Mathematics and Applications

2009

tom Vol. 31

29-36

By using the integral operator I(m) f, we introduce a class of holomorphic functions denoted by J(m)(α) and we obtain some superordinations results related to this class.

On Opial-type inequality for a generalized fractional integral operator

75%

Vivas-Cortez M. , Martínez F. , Valdes J. E. N. , Hernández J. E.

Demonstratio Mathematica

2022

tom Vol. 55, nr 1

695--709

This article is aimed at establishing some results concerning integral inequalities of the Opial type in the fractional calculus scenario. Specifically, a generalized definition of a fractional integral operator is introduced from a new Raina-type special function, and with certain results proposed in previous publications and the choice of the parameters involved, the established results in the work are obtained. In addition, some criteria are established to obtain the aforementioned inequalities based on other integral operators. Finally, a more generalized definition is suggested, with which interesting results can be obtained in the field of fractional integral inequalities.

New univalence criterions for special general integral operators

75%

Ebadian A. , Sokół J.

2013

tom Vol. 36

63--69

In this work we consider some integral operators on the special subclasses of the set of analytic functions in the unit disc which are defined by the Hadamard product. Using the univalence criterions, we obtain new sucient conditions for these operators to be univalent in the open unit disk. We give some applications of the main results.

An integral and MRAC-based approach to the adaptive stabilisation of a class of linear time-delay systems with unknown parameters

75%

Ramírez Jerónimo L. F. , Saldivar B. , Aguilar-Ibañez C. , Acosta J. Á.

International Journal of Applied Mathematics and Computer Science

2024

tom Vol. 34, no. 1

81--91

The design of a novel strategy based on the model reference adaptive control method for the stabilisation of a second-order linear time-delay system with unknown parameters is presented. The proposed approach is developed under the assumption that only one state of the system is available, and the sign of the control gain is known. First, the integral operator is applied to obtain a new representation of the original system, where the whole state is known. The use of the integral operator decomposes the control problem into two subproblems that are solved by using the model reference adaptive control method and the backstepping procedure. The effectiveness of the proposed approach is illustrated through an academic example and a practical application case regarding a chemical reactor recycle system.

A new iteration method for the solution of third-order BVP via Green's function

63%

Akgun F. A. , Rasulov Z.

tom Vol. 54, nr 1

425--435

In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.