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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]

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]

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 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]