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This paper aims to study qualitative properties and approximate solutions of a thermostat dynamics system with three-point boundary value conditions involving a nonsingular kernel operator which is called Atangana-Baleanu-Caputo (ABC) derivative for the first time. The results of the existence and uniqueness of the solution for such a system are investigated with minimum hypotheses by employing Banach and Schauder's fixed point theorems. Furthermore, Ulam-Hyers (UH) stability, Ulam-Hyers-Rassias UHR stability and their generalizations are discussed by using some topics concerning the nonlinear functional analysis. An efficiency of Adomian decomposition method (ADM) is established in order to estimate approximate solutions of our problem and convergence theorem is proved. Finally, four examples are exhibited to illustrate the validity of the theoretical and numerical results.

This paper considered theoretical and numerical methodologies.

This paper contains the following findings: (1) Thermostat fractional dynamics system is studied under ABC operator. (2) Qualitative properties such as existence, uniqueness and Ulam–Hyers–Rassias stability are established by fixed point theorems and nonlinear analysis topics. (3) Approximate solution of the problem is investigated by Adomain decomposition method. (4) Convergence analysis of ADM is proved. (5) Examples are provided to illustrate theoretical and numerical results. (6) Numerical results are compared with exact solution in tables and figures.

The novelty and contributions of this paper is to use a nonsingular kernel operator for the first time in order to study the qualitative properties and approximate solution of a thermostat dynamics system.

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

The objective of this work is to analyze the necessary conditions for chaotic behavior with fractional order and fractal dimension values of the fractal-fractional operator.

The numerical technique based on the fractal-fractional derivative is implemented over the fractional model and analyzes the condition at the distinct values of fractional order and fractal dimension.

The obtained numerical solution from the numerical technique is analyzed at distinct fractional order and fractal dimension values, and it has been figured out that the behavior of the solution either chaotic or non-chaotic agrees with the condition.

The necessary condition is associated with the fractional order only. So, our work not only studies the condition with fractional order but also examines the model by simultaneously adjusting fractal dimension values. It is found that the model still has chaotic or non-chaotic behavior at certain fractal dimension values and fractional order values corresponding to the condition.

The paper outlines a self-contained scheme for multiple networking agents at a location. It proposes a mathematical model for intelligent cloud entropy management systems. The purpose of this paper is to minimize the cost of system functionality by proposing the substantial use of a cloud-based system.

The paper proposes a hybrid cloud system, based on a fractional calculus of hybrid integral systems. Its discrete dynamics are suggested by using the fractional entropy type known as Tsallis entropy. This approach is based on the Wiener process (i.e. diffusion processes). This involves the net movement of information or data from a state of high meditation to a state of low observation. This property is a basic characteristic of hybrid cloud computing systems.

The paper offers a number of solutions to minimize the costs of cloud systems. The method is a proficient technique for presenting various types of fractional differential solutions.

Researchers are encouraged to test and modify the proposed method.

The paper includes suggestions for the expansion of a powerful method for managing and integrating cloud systems stably.

This paper addresses an acknowledged need to study how the cost function of cloud systems can be achieved.

Investigation of the smoking model is important as it has a direct effect on human health. This paper focuses on the numerical analysis of the fractional order giving up smoking model. Nonetheless, due to observational or experimental errors, or any other circumstance, it may contain some incomplete information. Fuzzy sets can be used to deal with uncertainty. Yet, there may be some inconsistency in the membership as well. As a result, the primary goal of this proposed work is to numerically solve the model in a type-2 fuzzy environment.

Triangular perfect quasi type-2 fuzzy numbers (TPQT2FNs) are used to deal with the uncertainty in the model. In this work, concepts of r2-cut at r1-plane are used to model the problem's uncertain parameter. The Legendre wavelet method (LWM) is then utilised to solve the giving up smoking model in a type-2 fuzzy environment.

LWM has been effectively employed in conjunction with the r2-cut at r1-plane notion of type-2 fuzzy sets to solve the model. The LWM has the advantage of converting the non-linear fractional order model into a set of non-linear algebraic equations. LWM scheme solutions are found to be well agreed with RK4 scheme solutions. The existence and uniqueness of the model's solution have also been demonstrated.

To deal with the uncertainty, type-2 fuzzy numbers are used. The use of LWM in a type-2 fuzzy uncertain environment to achieve the model's required solutions is quite fascinating, and this is the key focus of this work.

This paper aims to investigate the existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions. With regard to this nonlinear boundary value problem, three popular fixed point theorems, namely, Krasnoselskii’s theorem, Leray–Schauder’s theorem and Banach contraction principle, are employed to theoretically prove and guarantee three novel theorems. The main outcomes of this work are verified and confirmed via several numerical examples.

In order to accomplish our purpose, three fixed point theorems are applied to the problem under consideration according to some conditions that have been established to this end. These theorems are Krasnoselskii's theorem, Leray Schauder's theorem and Banach contraction principle.

In accordance to the applied fixed point theorems on our main problem, three corresponding theoretical results are stated, proved, and then verified via several numerical examples.

The existence and uniqueness of solution for generalized Sturm–Liouville and Langevin equations formulated using Caputo–Hadamard fractional derivative operator in accordance with three nonlocal Hadamard fractional integral boundary conditions are studied. To the best of the authors’ knowledge, this work is original and has not been published elsewhere.

The purpose of this paper is to obtain a numerical scheme for finding numerical solutions of linear and nonlinear Hadamard-type fractional differential equations.

The aim of this paper is to develop a numerical scheme for numerical solutions of Hadamard-type fractional differential equations. The classical Haar wavelets are modified to align them with Hadamard-type operators. Operational matrices are derived and used to convert differential equations to systems of algebraic equations.

The upper bound for error is estimated. With the help of quasilinearization, nonlinear problems are converted to sequences of linear problems and operational matrices for modified Haar wavelets are used to get their numerical solution. Several numerical examples are presented to demonstrate the applicability and validity of the proposed method.

The numerical method is purposed for solving Hadamard-type fractional differential equations.

This study aims to achieve the post-stall pitching maneuver (PSPM) and decrease the deflection frequency of aircraft actuators controlled by the robust backstepping method based on event-triggered mechanism (ETM), nonlinear disturbance observer (NDO) and dynamic surface control (DSC) techniques.

To estimate unsteady aerodynamic disturbances (UADs) to suppress their adverse effects, the NDO is designed. To avoid taking the derivative of the virtual control law directly and eliminate the coupling term of the system states and dynamic surface errors in the stability analysis, an improved DSC is developed. Combined with the NDO and DSC techniques, a robust backstepping method is proposed to achieve the PSPM. Furthermore, to decrease the deflection frequency of the aircraft actuators, a state-dependent ETM is introduced.

An ETM-and-NDO-based backstepping method with an improved DSC technique is developed to achieve the PSPM and decrease the deflection frequency of aircraft actuators. And simulation results are presented to verify the effectiveness of the proposed paper.

Few studies have been conducted on the control of the PSPM in which the lateral and longitudinal attitude dynamics are coupled with each other considering the UADs. Moreover, the mechanism that can decrease the deflection frequency of aircraft actuators is rarely developed in existing research. This study proposes an ETM-and-NDO-based backstepping scheme to address these problems with satisfactory performance of the PSPM.