In the present study, we have introduced the concept of Abel summability for sequences and series of fuzzy numbers. Also, some tauberian results in classical analysis have been generalized to fuzzy analysis.

Abel summability of sequences of fuzzy numbers

Fuzzy fractional differential equations with fuzzy coefficients are analyzed in the frame of Mikusinski operators. Systems of fuzzy operational algebraic equations are obtained, in view of the definition of fuzzy derivatives. Their exact and approximate solutions are constructed and their characters are analyzed, considering them as the corresponding solutions of the given problem. The described procedure of the construction of solutions is illustrated on an example and the obtained approximate solutions of the considered problems are visualized by using the GeoGebra software package.

On the operational solutions of fuzzy fractional differential equations

Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We derive uniform convergence of a fuzzy-valued function sequences and series with level sets. Also we study Hukuhara differentiation and Henstock integration of a fuzzy-valued function with some necessary inclusions. Furthermore, Fourier series of periodic fuzzy-valued functions is defined and its complex form is given via sine and cosine fuzzy coefficients with an illustrative example. Finally, by using the Dirichlet kernel and its properties, we especially examine the convergence of Fourier series of fuzzy-valued functions at each point of discontinuity, where one-sided limits exist.

https://downloads.hindawi.com/journals/tswj/2014/782652.pdf

On Fourier Series of Fuzzy-Valued Functions

In this paper, first the fuzzy generalized power series method, in which the coefficients are fuzzy numbers, is introduced, and then, the conditions of the uniqueness of the solution and its convergence for the fuzzy differential equation are investigated. Then, using the fuzzy generalized power series method, the fuzzy Legendre differential equation is considered as a case study, and finally, for further illustration some related examples are solved.

A fuzzy generalized power series method under generalized Hukuhara differentiability for solving fuzzy Legendre differential equation

In this paper, we construct the sets of bounded and continuous fuzzy-valued functions with the level sets. We investigate the relationships between these sets and their classical forms and give some properties including definitions, propositions and various kind of fuzzy distance functions. Furthermore, we study some of their properties like completeness, uniform convergence and differentiation and present two illustrative examples related to the complete and non-complete fuzzy metric spaces.

https://ispacs.com/journals/jfsva/2013/jfsva-00171/article.pdf

On the sets of fuzzy-valued function with the level sets

Following Talo and Basar (Determination of the duals of classical sets of sequences of fuzzy numbers and related matrix transformations, Comput. Math. Appl. 58 (2009) 717-733), we essentially deal with the power series of fuzzy numbers. We give two examples on the geometric series of fuzzy numbers and by using the four different cases of u n of n th power of a fuzzy number u, we interest in the convergence of a power series of fuzzy numbers. Finally, we introduce the concept of a power series of fuzzy numbers with fuzzy coefficients.

/pdf/power-series-of-fuzzy-numbers-with-real-or-fuzzy-2tocs3ta58.pdf

Uùgur Kadak

Papers

Power series of fuzzy numbers with real or fuzzy coefficients