Search Results (3)

In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative. Full article

We apply the Radu–Miheţ method derived from an alternative fixed-point theorem with a class of matrix-valued fuzzy controllers to approximate a fractional Volterra integro-differential equation with the $\psi$-Hilfer fractional derivative in matrix-valued fuzzy k-normed spaces to obtain an approximation for this type of fractional equation. Full article

The modeling of fuzzy fractional integro-differential equations is a very significant matter in engineering and applied sciences. This paper presents a novel treatment algorithm based on utilizing the fractional residual power series (FRPS) method to study and interpret the approximated solutions for a class of fuzzy fractional Volterra integro-differential equations of order $0<\beta \le 1$ which are subject to appropriate symmetric triangular fuzzy conditions under strongly generalized differentiability. The proposed algorithm relies upon the residual error concept and on the formula of generalized Taylor. The FRPS algorithm provides approximated solutions in parametric form with rapidly convergent fractional power series without linearization, limitation on the problem’s nature, and sort of classification or perturbation. The fuzzy fractional derivatives are described via the Caputo fuzzy $\mathrm{H}$ -differentiable. The ability, effectiveness, and simplicity of the proposed technique are demonstrated by testing two applications. Graphical and numerical results reveal the symmetry between the lower and upper $r$ -cut representations of the fuzzy solution and satisfy the convex symmetric triangular fuzzy number. Notably, the symmetric fuzzy solutions on a focus of their core and support refer to a sense of proportion, harmony, and balance. The obtained results reveal that the FRPS scheme is simple, straightforward, accurate and convenient to solve different forms of fuzzy fractional differential equations. Full article