In this paper, new intuitionistic fuzzy fixed point results for sequence of intuitionistic fuzzy set-valued maps in the structure of $b$-metric spaces are examined. A few nontrivial comparative examples are constructed to keep up the hypotheses and generality of our obtained results. Following the fact that most existing concepts of Ulam-Hyers type stabilities are concerned with crisp mappings, we introduce the notion of stability and well-posedness of functional inclusions involving intuitionistic fuzzy set-valued maps. It is a familiar fact that solution of every functional inclusion is a subset of an appropriate space. In this direction, intuitionistic fuzzy fixed point problem involving $(\alpha ,\beta )$-level set of an intuitionistic fuzzy set-valued map is initiated. Moreover, novel sufficient criteria for existence of solutions to an integral inclusion are investigated to indicate a possible application of the ideas presented herein.

We propose a new mathematical framework of generalized fractional-order to investigate the tuberculosis model with treatment. Under the generalized Caputo fractional derivative notion, the system comprises a network of five nonlinear differential equations. Besides that, the equilibrium points, stability and basic reproductive number are calculated. The concerned derivative involves a power-law kernel and, very recently, it has been adapted for various applied problems. The existence findings for the fractional-order tuberculosis model are validated using the Banach and Leray-Schauder nonlinear alternative fixed point postulates. For the developed framework, we have generated various forms of Ulam's stability outcomes. To investigate the estimated response and nonlinear behaviour of the system under investigation, the efficient mathematical formulation known as the $\mathrm{\wp }$-Laplace Adomian decomposition technique algorithm was implemented. It is important to mention that, with the exception of numerous contemporary discussions, spatial coherence was considered throughout the fractionalization procedure of the classical model. Simulation and comparison analysis yield more versatile outcomes than the existing techniques.

The aerodynamics analysis has grown in relevance for wind energy projects; this mechanism is focused on elucidating aerodynamic characteristics to maximize accuracy and practicability via the modelling of chaos in a wind turbine system's permanent magnet synchronous generator using short-memory methodologies. Fractional derivatives have memory impacts and are widely used in numerous practical contexts. Even so, they also require a significant amount of storage capacity and have inefficient operations. We suggested a novel approach to investigating the fractional-order operator's Lyapunov candidate that would do away with the challenging task of determining the indication of the Lyapunov first derivative. Next, a short-memory fractional modelling strategy is presented, followed by short-memory fractional derivatives. Meanwhile, we demonstrate the dynamics of chaotic systems using the Lyapunov function. Predictor-corrector methods are used to provide analytical results. It is suggested to use system dynamics to reduce chaotic behaviour and stabilize operation; the benefit of such a framework is that it can only be used for one state of the hybrid power system. The key variables and characteristics, i.e., the modulation index, pitch angle, drag coefficients, power coefficient, air density, rotor angular speed and short-memory fractional differential equations are also evaluated via numerical simulations to enhance signal strength.