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In this article, we will demonstrate some Hardy’s inequalities by utilizing Hölder inequality, integration by parts, and chain rule of the conformable fractional calculus. When α=1\alpha =1, we can obtain some of classical Copson’s and Hardy’s inequalities. In the end, we will obtain an application of Hardy’s inequality utilizing the conformable fractional calculus.

Background There are laboratory and clinical associations between liver and thyroid diseases. Hepatitis C virus is known to be responsible for both hepatic and extrahepatic diseases. Direct-acting antivirals (DAAs) provide high sustained viral response rates and much reduced adverse effects and impaired health-related quality of life during treatment. Aim To assess thyroid function in patients with chronic hepatitis C (CHC) receiving DAAs before start treatment and after achieving of SVR. Patients and methods A prospective study was conducted on 300 patients with CHC infection who were recruited for the study after obtaining written informed consent. Full history was taken, as well as routine examination and special investigations were done for all patients before the start of the remedy and by the end of treatment with DAAs. Results PCR results revealed a statistically significant difference, as SVR was evident in 98% of patients. Analysis of thyroid function assessments in the present study showed that 277 (92.3%) patients were euthyroid and 23 (7.7%) patients had thyroid disorders, comprising seven (2.3%) patients with subclinical hypothyroidism, 14 (4.66%) patients with overt hypothyroidism, and two (0.7%) patients with subclinical hyperthyroidism. Conclusion Thyroid function in patients with CHC infections was not damaged with treatment with DAAs for hepatitis C virus treatment. Hypothyroidism is prevalent in patients with CHC, and after treatment with DAAs, thyroid dysfunction slightly improved, especially subclinical, after achievement of SVR.

Aircraft pitch control system is one example of nonlinear complex systems which requires feedback control. Fuzzy logic controllers (FLC) have emerged as intelligent method in controlling such system by utilizing fuzzy logic principle. This paper presents a comparative analysis for the performance of proportional-derivative-integral (PID) controller and fuzzy logic controller in controlling the aircraft pitch angle. The input is the elevator deflection angle and the output is the pitch angle of the aircraft. For the fuzzy controller, it is governed by five membership functions and seventeen rules which were tuned repeatedly according to the actual output of the controller corresponding to the customized set point. The procedures of the PID and the FLC design are discussed in methodology section. In general, both PID and FLC perform within the design requirements. However, FLC outperforms PID in three design parameters namely the settling time, the percentage of overshoot and the steady state error, with improvements of 12%, 98% and 97%, respectively.

The oscillation and asymptotic behavior of solutions of a general class of damped second-order differential equations with several sub-linear neutral terms is considered. New sufficient conditions are established to fulfill a part of the gap in the oscillation theory for the case of sub-linear neutral equations. Our main results improve and generalize some of those recently published in the literature. Several examples are given to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we present novel advancements in the theory of bicomplex hypergeometric functions and their applications. We extend the hypergeometric function to bicomplex parameters, analyse its convergence region, and define its integral and derivative representations. Furthermore, we delve into the k-Riemann–Liouville fractional integral and derivative within a bicomplex operator, proving several significant theorems. The developed bicomplex hypergeometric functions and bicomplex fractional operators are demonstrated to have practical applications in various fields. This paper also highlights the essential concepts and properties of bicomplex numbers, special functions, and fractional calculus. Our results enhance the overall comprehension and possible applications of bicomplex numbers in mathematical analysis and applied sciences, providing a solid foundation for future research in this field. [ABSTRACT FROM AUTHOR]

This study explores the nonlinear Peyrard-Bishop DNA dynamic model, a nonlinear evolution equation that describes the behavior of DNA molecules by considering hydrogen bonds between base pairs and stacking interactions between adjacent base pairs. The primary objective is to derive analytical solutions to this model using the Khater III and improved Kudryashov methods. Subsequently, the stability of these solutions is analyzed through Hamiltonian system characterization. The Peyrard-Bishop model is pivotal in biophysics, offering insights into the dynamics of DNA molecules and their responses to external forces. By employing these analytical techniques and stability analysis, this research aims to enhance the understanding of DNA dynamics and its implications in fields such as drug design, gene therapy, and molecular biology. The novelty of this work lies in the application of the Khater III and an enhanced Kudryashov methods to the Peyrard-Bishop model, along with a comprehensive stability investigation using Hamiltonian system characterization, providing new perspectives on DNA molecule dynamics within the scope of nonlinear dynamics and biophysics [ABSTRACT FROM AUTHOR]

In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder's inequality, the chain rule, and the mean inequality. As specific instances of our findings (when T = N and T = R ), we obtain the discrete and continuous analogues of previously established inequalities. Additionally, we derive other inequalities for different time scales, such as T = q N 0 for q > 1 , which, to the best of the authors' knowledge, is a largely novel conclusion. [ABSTRACT FROM AUTHOR]

The objective of this article is to examine, stabilize, and linearize the incompressible magnetohydrodynamic model equations. The approximate solutions are carried out through the lowest equal order mixed finite element (FE) approach, involving variables such as fluid velocity, hydro pressure, magnetic field, and magnetic pressure. The formulation of the variational form for the approximate solution necessitates the use of a pair of approximating spaces. However, these spaces cannot be arbitrarily chosen; they must adhere to strict stability conditions, notably the Ladyzhenskaya–Babuska–Brezzi (LBB) or inf-sup condition. This study addresses the absence of stabilization and linearization techniques in the incompressible magnetohydrodynamic model equations using the lowest equal order mixed finite element approach. The article introduces a stabilization technique to meet two stability conditions, proving its existence and uniqueness. This novel approach was not previously explored in the literature. The proposed stabilized technique does not necessitate parameters or computing higher-order derivatives, making it computationally efficient. The study offers numerical tests demonstrating optimal convergence and effectiveness of the revised approach in two-dimensional settings. [ABSTRACT FROM AUTHOR]

This paper presents novel criteria for investigating the oscillatory behavior of even-order neutral differential equations. By employing a comparative approach, we established the oscillation properties of the studied equation through comparisons with well-understood first-order equations with known oscillatory behavior. The findings of this study introduce fresh perspectives and enrich the existing body of oscillation criteria found in the literature. To illustrate the practical application of our results, we provide an illustrative example. [ABSTRACT FROM AUTHOR]

In this article, we establish some new generalized inequalities of the Hilbert-type on time scales' delta calculus, which can be considered similar to formulas for inequalities of Hilbert type. The major innovation point is to establish some dynamic inequalities of the Hilbert-type on time scales' delta calculus for delta differentiable functions of one variable and two variables. In this paper, we use the condition  a j (s j) = 0  and  a j (s j , z j) = a j (w j , n j) = 0 ,  ∀ j = 1 , 2 , ... , n . These inequalities will be proved by applying Hölder's inequality, the chain rule on time scales, and the mean inequality. As special cases of our results (when  T = N  and  T = R ), we obtain the discrete and continuous inequalities. Also, we can obtain other inequalities in different time scales, like  T = q Z − ,  q > 1 . [ABSTRACT FROM AUTHOR]

Through the paper, we present several inequalities involving C-monotonic functions with C ≥ 1 , on nabla calculus via time scales. It is known that dynamic inequalities generate many different inequalities in different calculus. The main results will be proved by applying the chain rule formula on nabla calculus. As a special case for our results, when T = R , we obtain the continuous analouges of inequalities that had previously been proved in the literature. When T = N , the results, to the best of the authors' knowledge, are essentially new. Symmetrical properties of C -monotonic functions are critical in determining the best way to solve inequalities. [ABSTRACT FROM AUTHOR]