On Graphical Fuzzy Metric Spaces with Application to Fractional Differential Equations

FUZZY FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN PARTIALLY ORDERED METRIC SPACES

In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via  weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.

System of fuzzy fractional differential equations in generalized metric space

In this paper, we study the existence of integral solutions of fuzzy fractional differential systems with nonlocal conditions under Caputo generalized Hukuhara derivatives. These models are considered in the framework of completegeneralized metric spaces in the sense of Perov. The novel feature of our approach is the combination of the convergentmatrix technique with Schauder fixed point princi...

Fuzzy Local Fractional Differential Equations

A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

and Applied Analysis 3 Besides, if for any x, y ∈ M, there exists z ∈ M which is comparable to x and y, 2.4 then f has a unique fixed point. Proof. We first show that f has a fixed point. Since x0 f x0 and f is an increasing function, we obtain by induction that x0 f x0 f2 x0 f3 x0 · · · f x0 · · · . 2.5 Put xn 1 f x0 , n 1, 2, . . . For each integer n ≥ 1, from 2.5 , we have xn xn 1, then by 2...

The fuzzy generalized Taylor’s expansion with application in fractional differential equations

In this paper, the generalized Taylor’s expansion is presented for fuzzy-valued functions. To achieve this aim, fuzzyfractional mean value theorem for integral, and some properties of Caputo generalized Hukuhara derivative are necessarythat we prove them in details. In application, the fractional Euler’s method is derived for solving fuzzy fractionaldifferential equations in the sense of Caputo...