A. Sami Bataineh
YOU?
Author Swipe
View article: A general definition of the fractal derivative: Theory and applications
A general definition of the fractal derivative: Theory and applications Open
In this paper, we introduce a general definition of the fractal derivative with respect to a function $ \psi $, in the context of the order $ 0 < \alpha\leq 1 $ and the function $ \psi(\Theta) $. This novel definition generalizes the class…
View article: Implementing a Solar Panel System at King Hamad University Hospital: A Pathway to Sustainability and Cost Efficiency
Implementing a Solar Panel System at King Hamad University Hospital: A Pathway to Sustainability and Cost Efficiency Open
Purpose: This paper analyses the functioning of a solar panel system at King Hamad University Hospital (KHUH), indicating its part in enhancing sustainability and cost-efficiency. Due to the increasing demand in renewable energy, this stud…
View article: The general Bernstein function: Application to χ‐fractional differential equations
The general Bernstein function: Application to χ‐fractional differential equations Open
In this paper, we present the general Bernstein functions for the first time. The properties of generalized Bernstein basis functions are given and demonstrated. The classical Bernstein polynomial bases are merely a subset of the general B…
View article: A cotangent fractional Gronwall inequality with applications
A cotangent fractional Gronwall inequality with applications Open
This article presents the cotangent fractional Gronwall inequality, a novel understanding of the Gronwall inequality within the context of the cotangent fractional derivative. We furnish an explanation of the cotangent fractional derivativ…
View article: Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms
Oscillatory Behavior of Higher-Order Differential Equations with Delay Terms Open
The aim of this research is to study the oscillatory properties of higher -order delay half linear differential equations with non-canonical operators. Two methods for establishing some new conditions for the oscillation of all solutions o…
View article: The Novel Mittag-Leffler–Galerkin Method: Application to a Riccati Differential Equation of Fractional Order
The Novel Mittag-Leffler–Galerkin Method: Application to a Riccati Differential Equation of Fractional Order Open
We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called the Mittag-Leffler–Galerkin method—comprises the finite Mittag-Leffler function and the Galerkin method. The erro…
View article: Oscillation Criteria of Fourth-Order Differential Equations with Delay Terms
Oscillation Criteria of Fourth-Order Differential Equations with Delay Terms Open
The aim of this paper is to derive oscillation criteria of the following fourth-order differential equation with delay term r x z ′ ′ ′ x γ ′ + ∑ i = 1 n q i x f z η i x …
View article: Bernstein Collocation Method for Solving MHD Jeffery–Hamel Blood Flow Problem with Error Estimations
Bernstein Collocation Method for Solving MHD Jeffery–Hamel Blood Flow Problem with Error Estimations Open
In this paper, the Bernstein collocation method (BCM) is used for the first time to solve the nonlinear magnetohydrodynamics (MHD) Jeffery–Hamel arterial blood flow issue. The flow model described by nonlinear partial differential equation…
View article: An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs
An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs Open
In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of…
View article: An Efficient Scheme for Time-Dependent Emden-Fowler Type Equations Based on Two-Dimensional Bernstein Polynomials
An Efficient Scheme for Time-Dependent Emden-Fowler Type Equations Based on Two-Dimensional Bernstein Polynomials Open
In this study, we introduce an efficient computational method to obtain an approximate solution of the time-dependent Emden-Fowler type equations. The method is based on the 2D-Bernstein polynomials (2D-BPs) and their operational matrices.…
View article: Multistage Bernstein collocation method for solving strongly nonlinear damped systems
Multistage Bernstein collocation method for solving strongly nonlinear damped systems Open
In this paper, we propose an approximate solution method, called multistage Bernstein collocation method (MBCM), to solve strongly nonlinear damped systems. The method is given with an error analysis. The systems investigated include step …
View article: Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function
Bernstein polynomials method and it’s error analysis for solving nonlinear problems in the calculus of variations: Convergence analysis via residual function Open
In this paper, Bernstein polynomials method (BPM) and their operational matrices are adopted to obtain approximate analytical solutions of variational problems. The operational matrix of differentiation is introduced and utilized to reduce…
View article: Application of Adaptation HAM for Nonlinear Oscillator Typified as A Mass Attached to A Stretched Elastic Wire
Application of Adaptation HAM for Nonlinear Oscillator Typified as A Mass Attached to A Stretched Elastic Wire Open
This paper applies the adaptation of homotopy analysis method (AHAM) for the first time to obtained the periodic solutions for the oscillation of a mass attached to a stretched elastic wire. The AHAM approach can be applied directly to the…
View article: Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall
Bernstein method for the MHD flow and heat transfer of a second grade fluid in a channel with porous wall Open
In this paper, we present an approximate solution method for the problem of magnetohydrodynamic (MHD) flow and heat transfer of a second grade fluid in a channel with a porous wall. The method is based on the Bernstein polynomials with the…
View article: On the approximate solutions of systems of odes by legendre operational matrix of differentiation
On the approximate solutions of systems of odes by legendre operational matrix of differentiation Open
In this article, a general framework for solving system of ordinary differential equations by implementing a relatively new numerical technique called the Legendre operational matrix of differentiation is presented for the first time. This…