A. A. Karaballi

Bio: A. A. Karaballi is an academic researcher from Kuwait University. The author has contributed to research in topics: Differential equation & Quartic function. The author has an hindex of 5, co-authored 10 publications receiving 575 citations.

Analytical investigations of the sumudu transform and applications to integral production equations

Abstract: The Sumudu transform, whose fundamental properties are presented in this paper, is little known and not widely used However, being the theoretical dual to the Laplace transform, the Sumudu transform rivals it in problem solving Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain Here, we use it to solve an integral production-depreciation problem

Sumudu transform fundamental properties investigations and applications.

Abstract: The Sumudu transform, whose fundamental properties are presented in this paper, is still not widely known, nor used. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. In 2003, Belgacem et al. have shown it to be the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving. Here, using the Laplace-Sumudu duality (LSD), we avail the reader with a complex formulation for the inverse Sumudu transform. Furthermore, we generalize all existing Sumudu differentiation, integration, and convolution theorems in the existing literature. We also generalize all existing Sumudu shifting theorems, and introduce new results and recurrence results, in this regard. Moreover, we use the Sumudu shift theorems to introduce a paradigm shift into the thinking of transform usage, with respect to solving differential equations, that may be unique to this transform due to its unit-preserving properties. Finally, we provide a large and more comprehensive list of Sumudu transforms of functions than is available in the literature.

Extended double-stride L-stable methods for the numerical solution of ODEs

Abstract: Usmani and Agarwal [1] had proposed construction of extended one-step higher (than two) order A-stable methods by coupling classical Linear Multistep Methods (LMMs). Following on their idea, in the present paper we describe a class of extended double-stride methods based on Simpson's rule, which are fourth order and L-stable.

Sumudu transform fundamental properties investigations and applications.

Abstract: The Sumudu transform, whose fundamental properties are presented in this paper, is still not widely known, nor used. Having scale and unit-preserving properties, the Sumudu transform may be used to solve problems without resorting to a new frequency domain. In 2003, Belgacem et al. have shown it to be the theoretical dual to the Laplace transform, and hence ought to rival it in problem solving. Here, using the Laplace-Sumudu duality (LSD), we avail the reader with a complex formulation for the inverse Sumudu transform. Furthermore, we generalize all existing Sumudu differentiation, integration, and convolution theorems in the existing literature. We also generalize all existing Sumudu shifting theorems, and introduce new results and recurrence results, in this regard. Moreover, we use the Sumudu shift theorems to introduce a paradigm shift into the thinking of transform usage, with respect to solving differential equations, that may be unique to this transform due to its unit-preserving properties. Finally, we provide a large and more comprehensive list of Sumudu transforms of functions than is available in the literature.

A theoretical study of the Caputo-Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control

Abstract: Mumps is the most common cause of acquired unilateral deafness in children, in which hearing loss occurs at all auditory frequencies. We use a box model to model hearing loss in children caused by the mumps virus, and since the fractional-order derivative retains the effect of system memory, we use the Caputo–Fabrizio fractional derivative in this modeling. In the beginning, we compute the basic reproduction number R 0 and equilibrium points of the system and investigate the stability of the system at the equilibrium point. By utilizing the Picard–Lindelof technique, we prove the existence an unique solution for given fractional CF -system of hearing loss model and investigate the stability of iterative method by fixed point theory. The optimal control of the system is determined by considering the treatment as a control strategy to reduce the number of infected people. Using the Euler method for the fractional-order Caputo–Fabrizio derivative, the approximate solution of the system is calculated. We present a numerical simulation for the transmission of disease with respect to the transmission rate and the basic reproduction number in two cases R 0 1 and R 0 > 1 . To investigate the effect of fractional order derivative on the behavior and value of each of the variables in Model 2, we calculate the results for several fractional order derivatives and compare the results. Also, considering the importance of reproduction number in the continuation of disease transmission, we analyze the sensitivity of R 0 respect to each of the model parameters and determine the impact of each parameter.

Analysis of the model of HIV-1 infection of CD4+$CD4^{+}$ T-cell with a new approach of fractional derivative

Abstract: By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.

An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma

Abstract: In this paper, we present a coupling of homotopy perturbation technique and sumudu transform known as homotopy perturbation sumudu transform method (HPSTM). We show applicability of this method by solving fractional equal width (EW) equation, fractional modified equal width (MEW) equation and variant of fractional modified equal width (VMEW) equation. The fractional equal width equations play a key role in describing hydro-magnetic waves in cold plasma. Our aim is to study the nonlinear behavior of plasma system and highlight the important points. We examine the ability of HPSTM to study the fractional nonlinear systems and show its supremacy over other available numerical techniques. The other key point of this investigation is to examine two important fractional equations with different nonlinearity. The HPSTM gives excellent accuracy in analogous with the numerical solution. The numerical solutions indicate that the HPSTM is a powerful technique for studying the nonlinear behavior of plasma system very precisely and accurately.

A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

Abstract: We present a fractional-order model for the COVID-19 transmission with Caputo–Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.