•Journal•ISSN: 1110-757X
Journal of Applied Mathematics
Hindawi Publishing Corporation
About: Journal of Applied Mathematics is an academic journal published by Hindawi Publishing Corporation. The journal publishes majorly in the area(s): Nonlinear system & Boundary value problem. It has an ISSN identifier of 1110-757X. It is also open access. Over the lifetime, 3590 publications have been published receiving 33453 citations.
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TL;DR: In this survey paper, nearly all types of Mittag-Leffler type functions existing in the literature are presented and an attempt is made to present nearly an exhaustive list of references to make the reader familiar with the present trend of research in Mittag, Leffler, and type functions and their applications.
Abstract: Motivated essentially by the success of the applications of the Mittag-Leffler functions in many areas
of science and engineering, the authors present, in a unified manner, a detailed account or rather a brief
survey of the Mittag-Leffler function, generalized Mittag-Leffler functions, Mittag-Leffler type functions,
and their interesting and useful properties. Applications of G. M. Mittag-Leffler functions in certain areas of
physical and applied sciences are also demonstrated. During the last two decades this function has come
into prominence after about nine decades of its discovery by a Swedish Mathematician Mittag-Leffler,
due to the vast potential of its applications in solving the problems of physical, biological, engineering, and
earth sciences, and so forth. In this survey paper, nearly all types of Mittag-Leffler type functions existing in the
literature are presented. An attempt is made to present nearly an exhaustive list of references concerning
the Mittag-Leffler functions to make the reader familiar with the present trend of research in Mittag-Leffler
type functions and their applications.
661 citations
TL;DR: This paper proposes dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy Sets, hesitant fuzzy set, and fuzzy multisets as special cases, and investigates the basic operations and properties of DHFSs.
Abstract: In recent decades, several types of sets, such as fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type 2 fuzzy sets, type 𝑛 fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. In this paper, we propose dual hesitant fuzzy sets (DHFSs), which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets as special cases. Then we investigate the basic operations and properties of DHFSs. We also discuss the relationships among the sets mentioned above, use a notion of nested interval to reflect their common ground, then propose an extension principle of DHFSs. Additionally, we give an example to illustrate the application of DHFSs in group forecasting.
540 citations
TL;DR: This paper examines the forecasting performance of ARIMA and artificial neural networks model with published stock data obtained from New York Stock Exchange to reveal the superiority of Neural networks model over ARimA model.
Abstract: This paper examines the forecasting performance of ARIMA and artificial neural networks model with published stock data obtained from New York Stock Exchange. The empirical results obtained reveal the superiority of neural networks model over ARIMA model. The findings further resolve and clarify contradictory opinions reported in literature over the superiority of neural networks and ARIMA model and vice versa.
381 citations
TL;DR: In this paper, a numerical Laplace transform algorithm based on the decomposition method is introduced for the approximate solution of a class of nonlinear differential equations, which is rapidly convergent and quite accurate by which it approximates the solution using only few terms of its iterative scheme.
Abstract: In this paper, a numerical Laplace transform algorithm which is based on the decomposition method is introduced for the approximate solution of a class of nonlinear differential equations. The technique is described and illustrated with some numerical examples. The results assert that this scheme is rapidly convergent and quite accurate by which it approximates the solution using only few terms of its iterative scheme.
306 citations
TL;DR: It is demonstrated that the performance of this hybrid metaheuristic method (HS/BA) is superior to, or at least highly competitive with, the standard BA and other population-based optimization methods, such as ACO, BA, BBO, DE, ES, GA, HS, PSO, and SGA.
Abstract: A novel robust hybrid metaheuristic optimization approach, which can be considered as an improvement of the recently developed bat algorithm, is proposed to solve global numerical optimization problems. The improvement includes the addition of pitch adjustment operation in HS serving as a mutation operator during the process of the bat updating with the aim of speeding up convergence, thus making the approach more feasible for a wider range of real-world applications. The detailed implementation procedure for this improved metaheuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most situations, the performance of this hybrid metaheuristic method (HS/BA) is superior to, or at least highly competitive with, the standard BA and other population-based optimization methods, such as ACO, BA, BBO, DE, ES, GA, HS, PSO, and SGA. The effect of the HS/BA parameters is also analyzed.
286 citations