Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions.
In this paper, we investigate the classical sets of sequences of fuzzy numbers by using partial metric which is based on a partial ordering. Some elementary notions and concepts for partial metric and fuzzy level sets are given. In addition, several necessary and sufficient conditions for partial completeness are established by means of fuzzy level sets. Finally, we give some illustrative examples and present some results between fuzzy and partial metric spaces.
In this paper we study the existence and uniqueness of weak solutions of the g-Bénard problem. Then, we investigate the long-term dynamics; specically, we derive upper bounds for the number of determining modes for this system.
In this paper, we essentially deal with
Köthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh's
extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct
some classical notions. In this paper, we present the sets of bounded, convergent, and null series and the
set of sequences of bounded variation of fuzzy level sets, based on the partial metric. We examine the
relationships between these sets and their classical forms and give some properties including definitions,
propositions, and various kinds of partial metric spaces of fuzzy level sets. Furthermore, we study some of
their properties like completeness and duality. Finally, we obtain the Köthe-Toeplitz duals of fuzzy level
sets with respect to the partial metric based on a partial ordering.
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