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This paper is concerned with the existence of mild solutions and total controllability for a class of non-autonomous measure evolution systems with non-instantaneous impulses and state-dependent delay. By using the theory of evolution family and Krasnoselskii’s fixed point theorem, the existence of mild solutions and total controllability for the considered systems is obtained. Finally, we give two applications to support the validity of the study.

The main metabolism of yeasts produces bioethanol. Bioethanol, which is produced from biomass and bioenergy crops, has been promoted as one of the most viable alternatives to fossil fuels. The following reaction represents all of the knowledge we have regarding intracellular reactions and their regulatory mechanisms: biomass+substrates→ethanol+biomass(morecells). Atangana has suggested new operators based on a combination of fractional and fractal calculus. Fractal-fractional operators (FFOs) have frequently been utilized to investigate the dynamics of a physical problem. In this paper, FFOs are used to investigate a nonlinear mathematical model for ethanol production with three different kernels. Famous fixed point results are employed to show the existence and uniqueness of the solution of the FFO ethanol model under the Mittag–Leffler kernel. The concept of non-linear analysis is utilized to demonstrate the model’s Ulam–Hyres stability. The Adams—Bashforth numerical technique, which is based on the Lagrangian interpolation method, is utilized to find the solution of the model under fractal-fractional operators with three different kernels. The numerical results are simulated with MATLAB-17 for several sets of fractional orders and fractal dimensions to show the relationship between components of ethanol production under new operators in various senses.

In this paper, we define multi-fuzzy Banach algebra and then prove the stability of involution on multi-fuzzy Banach algebra by fixed point method. That is, if f:A→A is an approximately involution on multi-fuzzy Banach algebra A, then there exists an involution H:A→A which is near to f. In addition, under some conditions on f, the algebra A has multi C*-algebra structure with involution H.

In this paper, fixed point theorems using ψ contractive mapping in C∗-algebra valued b-metric space are introduced. By stating multiple scenarios that illustrate the application domains, we demonstrate several applications from the obtained results. In particular, we begin with the definition of the positive function and then recall some properties of the function that lay the fundamental basis for the research. We then study some fixed point theorems in the C∗-algebra valued b-metric space using a positive function.

In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented.

In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.