Search

Within the confines of a two-fluid quantum magnetohydrodynamic model, the investigation of magnetoacoustic shock and solitary waves is conducted in an electron-ion magnetoplasma that considers electrons of spin 1/2. When the plasma system is nonlinearly investigated using the reductive perturbation approach, the Korteweg de Vries-Burgers (KdVB) equation is produced. Sagdeev's potential is created, revealing the presence of solitary solutions. However, when dissipative terms are included, intriguing physical solutions can be obtained. The KdVB equation is further investigated using the phase plane theory of a planar dynamical system to demonstrate the existence of periodic and solitary wave solutions. Predicting several classes of traveling wave solutions is advantageous due to various phase orbits, which manifest as soliton-shock waves, and oscillatory shock waves. The presence of a magnetic field, the density of electrons and ions, and the kinematic viscosity significantly alter the properties of magnetoacoustic solitary and shock waves. Additionally, electric fields have been identified. The outcomes obtained here can be applied to studying the nature of magnetoacoustic waves that are observed in compact astrophysical environments, where the influence of quantum spin phenomena remains significant, and also in controlled laboratory plasma experiments. [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 paper, we introduce ten new quadruple hypergeometric series. We also obtain their various properties such that integral representations, fractional derivatives, N-fractional connections, operational relations and generating functions. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop the Fibonacci wavelet method together with the quasi‐linearization technique to solve the fractional‐order logistic growth model. The block‐pulse functions are employed to construct the operational matrices of fractional‐order integration. The fractional derivative is described in the Caputo sense. The present time‐fractional population growth model is converted into a set of nonlinear algebraic equations using the proposed generated matrices. Making use of the quasi‐linearization technique, the underlying equations are then changed to a set of linear equations. Numerical simulations are conducted to show the reliability and use of the suggested approach when contrasted with methods from the existing literature. A comparison of several numerical techniques from the available literature is presented to show the efficacy and correctness of the suggested approach. [ABSTRACT FROM AUTHOR]

In this paper, by applying Pachpatte's type integral inequality with integral impulses, we investigate Ulam–Hyers and Ulam–Hyers–Rassias stabilities for the impulsive Volterra delay integrodifferential equation Banach spaces. Suitable examples are given to support the obtained results. [ABSTRACT FROM AUTHOR]

The coupled fractional Fourier transform is a much recent ramification of the two-dimensional fractional Fourier transform, wherein the kernel is not a tensor product of one-dimensional copies, but relies on two angles that are coupled to yield a new pair of transform parameters. In this paper, we introduce a novel two-dimensional Wigner distribution, coined as coupled fractional Wigner distribution (CFrWD). The prime advantage of such a ramification of the Wigner distribution lies in the fact that the CFrWD can efficiently tackle the higher-order-phase and chirp signals, which constitute a wider class of signals arising in modern communication systems. To begin with, we study some fundamental properties of the proposed CFrWD, including marginal, shifting, conjugate-symmetry and anti-derivative properties. In addition, we also formulate the Moyal's principle, inversion formula and the convolution and correlation theorems associated with CFrWD. Nevertheless, we demonstrate the efficacy of CFrWD for estimating and detecting both the one-component and multi-component linear-frequency-modulated signals. [ABSTRACT FROM AUTHOR]

In this article, a novel collocation method is developed based on Gegenbauer wavelets together with the quasi‐linearization technique to facilitate the solution of population growth model of fractional order in a closed system. The operational matrices of fractional order integration are obtained via block‐pulse functions. The obtained matrices are employed to transform the given time‐fractional population growth model into a non‐linear system of algebraic equations. Then, the quasi‐linearization technique is invoked to convert the underlying equations to a linear system of equations. The performance and accuracy of the proposed method is elucidated by a presenting a comparison with some numerical methods existing in the open literature. The numerical outcomes shows that the present method is more efficient than the existing ones. [ABSTRACT FROM AUTHOR]

In this paper, we have obtained an approximate solution of multi-term Caputo fractional differential equations (MFDEs) using the Variational iteration method (VIM). Further, we have obtained the convergence criteria and error approximation of VIM for solving generalized multi term fractional differential equations. The obtained results are shown using plots to demonstrated the efficiency and accuracy of the VIM. [ABSTRACT FROM AUTHOR]

The dual solutions for the stagnation point flow in a cobalt–CeO2/kerosene hybrid nanofluid with melting heat transfer and thermal radiation are analyzed. The partial differential equations are solved by the conversion of the partial differential equations into nonlinear ordinary differential equations by utilizing suitable scaling group transformations. Numerical solutions are obtained by employing the built-in function in the MATLAB software (bvp4c). Physically recoverable solutions are found employing stability analysis. The factor variables of interest (melting parameter, the nanoparticle volume fraction of cobalt and CeO2) are then further analyzed by utilizing the sensitivity analysis (based on the response surface methodology model) for heat transfer rate, as well as the skin friction coefficient. It is found that the heat transfer and skin friction tend to be significantly higher in a hybrid nanofluid due to the radiation and melting heat transfer. The lower branch is found to be unstable, whereas the upper branch is found to be stable. Also, the heat transfer rate and skin friction coefficient are found to be negatively sensitive toward the melting parameter. The model in this study can be applied for microscopic propulsion systems and the nano-electromechanical systems integrated with a nano-based system. [ABSTRACT FROM AUTHOR]

In this paper, we develop an efficient wavelet method based on the Fibonacci polynomials for solving the Pennes bioheat transfer equation. The formulation of the proposed technique is started with the construction of Fibonacci wavelets by using Fibonacci polynomials and then applying spectral collocation technique to transform the given problem into a system of an algebraic equation, that can be solved using the Newton method. Some results related to error estimate and convergence analysis of the proposed scheme are also investigated. The applicability and accuracy of the present technique are elucidated by a comparison with the exact solution and those of the other methods found in the recent literature. The obtained results show that the proposed technique is an effective tool for solving Pennes bioheat transfer equations and can also be used for solving similar types of various partial differential equations numerically. [ABSTRACT FROM AUTHOR]

The effects of thermophoretic motion and viscous dissipation on the two-dimensional fluid flowing along different positions of a sphere are inspected by considering slip flow. The leading set of partial differential equations is altered as a set of nonlinear primitive partial differential equations utilizing primitive variable transformation. The finite difference method is used to solve the governing equations numerically. The impacts of appropriate parameters, such as Eckert number slip flow parameters, mixed convection parameter, and thermophoresis parameter on unknown variables, such as velocity profile, mass concentration, and temperature profile are analyzed and displayed with the help of graphs by using the highly technical software, Tecplot 360. And also, we have observed the effects of the identical parameters on skin friction coefficient, rate of heat, and rate of mass transfers by means of graphs. From the outcomes, we noted that (a) the velocity profile is dominant at position 𝑋=1.5 rad and the temperature distribution and mass concentration are dominant at position 𝑋=𝜋 rad for increasing values of Eckert number. (b) Slip parameter boosts the velocity at position 𝑋=2.095 rad but temperature and mass concentration are maximum at position 𝑋=𝜋 rad. (c) The thermophoretic parameter is also having a very strong impact on heat and fluid flow mechanics. The slip flow provides benefits in improving heat and mass transfer mechanisms along with skin friction. It is also predicted that the concentration boundary layer will be thinner during thermophoresis around the different positions. The novelty of the predicted work is holding slip flow with the inclusion of mechanical energy and thermophoretic motion around different positions of the sphere. It is worth mentioning that the obtained results predicted in graphs are satisfied by the prescribed boundary conditions, which yield the corrected skin friction, rate of heat transfer, and rate of mass transfer. [ABSTRACT FROM AUTHOR]

The quadratic‐phase Fourier transform (QPFT) is a recent addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier transform. In this article, we formulate several classes of uncertainty principles for the QPFT. Firstly, we formulate the Heisenberg's uncertainty principle governing the simultaneous localization of a signal and the corresponding QPFT. Secondly, we obtain some logarithmic and local uncertainty inequalities such as Beckner and Sobolev inequalities for the QPFT. Thirdly, we study several concentration‐based uncertainty principles, including Nazarov's, Amrein–Berthier–Benedicks's, and Donoho–Stark's uncertainty principles. Finally, we conclude the study with the formulation of Hardy's and Beurling's uncertainty principles for the QPFT. [ABSTRACT FROM AUTHOR]

The impact of Stefan blowing on the MHD bioconvective slip flow of a nanofluid towards a sheet is explored using numerical and statistical tools. The governing partial differential equations are nondimensionalized and converted to similarity equations using apposite transformations. These transformed equations are solved using the Runge–Kutta–Fehlberg method with the shooting technique. Graphical visualizations are used to scrutinize the effect of the controlling parameters on the flow profiles, skin friction coefficient, local Nusselt, and Sherwood number. Moreover, the sensitivities of the reduced Sherwood and Nusselt number to the input variables of interest are explored by adopting the response surface methodology. The outcomes of the limiting cases are emphatically in corroboration with the outcomes from preceding research. It is found that the heat transfer rate has a positive sensitivity towards the haphazard motion of the nanoparticles and a negative sensitivity towards the thermomigration. The thermal field is enhanced by the Stefan blowing aspect. Moreover, the fluid velocity can be controlled by the applied magnetic field. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigate some existence and uniqueness results of integrable solutions for nonlinear fractional order initial value differential equations involving Caputo operator. We develop the existence of integral solution using Schauder's fixed point theorem. In addition, by applying the Banach contraction principle, we establish uniqueness result. To illustrate the applicability of main results, two examples are presented. [ABSTRACT FROM AUTHOR]

The Euler, Laplace, Whittaker and fractional Fourier transforms of k-Bessel function is established in this paper. The results obtained here are expressed in terms of generalized Wright function. [ABSTRACT FROM AUTHOR]