In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order κ and investigate the existence of a unique solution in matrix-valued fuzzy Banach spaces for this equation using the alternative fixed point theorem. In a fuzzy environment, we introduce a class of the matrix-valued fuzzy Wright controller to investigate the Hyers–Ulam–Wright stability for the NH-FD-O equation with order κ. Finally, an illustrative example to demonstrate the application of the main theorem is also considered.

In the current article, we define the multicubic–quartic mappings and describe them as an equation. We also study n-variable mappings, which are mixed type cubic–quartic in each variable and then give a characterization of such mappings. Indeed, we unify the general system of cubic–quartic functional equations defining a multimixed cubic–quartic mapping to a single equation, say, the multimixed cubic–quartic functional equation. Furthermore, we show under what conditions every multimixed cubic–quartic mapping can be multicubic, multiquartic and multicubic–quartic. In addition, by means of a known fixed-point result, we prove the Găvrua stability of multimixed cubic–quartic functional equations in the setting of quasi-β-normed spaces. One of the important results is that every multimixed cubic–quartic functional equation on a quasi-β-normed space is the Hyers–Ulam stable. Lastly, we investigate the hyperstability of multicubic $\ast$-derivations on $C^{\ast }$-algebras.

There are some confusion and complexity in our everyday lives, as we live in an uncertain environment. In such type of environment, an accurate calculation of the data and finding a solution to a problem is not an easy job. So, fuzzy differential equations are the better tools to model problems in the fuzzy domain. Modeling the real-world phenomenon more accurately requires such operators. Therefore, we investigate the fractional-order Swift–Hohenberg equation in the fuzzy concept. We study this equation under the fuzzy Caputo fractional derivative. We use the fuzzy Sumudu transform to find out the semianalytical solution of the considered equation. To deal with the nonlinear term of the problem, we also use the Adomian decomposition method. To confirm the accuracy of the proposed procedure, we give two test problems. Lastly, we plot the numerical results for various fractional orders, and uncertainty belongs to [0, 1].

The general fractional conformable derivative (GCD) and its attributes have been described by researchers in the recent times. Compared with other fractional derivative definitions, this derivative presents a generalization of the conformable derivative and follows the same derivation formulae. For electrical circuits, such as RLC, RC, and LC, we obtain a new class of fractional-order differential equations using this novel derivative, The use of GCD to depict electrical circuits has been shown to be more adaptable and lucrative than the usual conformable derivative.