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131 results on '"Alshomrani, Ali S."'

21. Fractional hyper-chaotic system with complex dynamics and high sensitivity: Applications in engineering.

Author

Partohaghighi, Mohammad, Yusuf, Abdullahi, Alshomrani, Ali S., Sulaiman, Tukur Abdulkadir, and Baleanu, Dumitru

Subjects
SYSTEM dynamics, FIXED point theory, FINITE differences, ENGINEERING, HYPERGRAPHS
Abstract

Hyper-chaotic systems have useful applications in engineering applications due to their complex dynamics and high sensitivity. This research is supposed to introduce and analyze a new noninteger hyper-chaotic system. To design its fractional model, we consider the Caputo fractional operator. To obtain the approximate solutions of the extracted system under the considered fractional-order derivative, we employ an accurate nonstandard finite difference (NSFD) algorithm. Moreover, the existence and uniqueness of the solutions are provided using the theory of fixed-point. Also, to see the performance of the utilized numerical scheme, we choose different values of fractional orders along with various amounts of the initial conditions (ICs). Graphs of solutions for each case are provided. [ABSTRACT FROM AUTHOR]

Published
2024
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28. Nonlinear wave train in an inhomogeneous medium with the fractional theory in a plane self-focusing

Author

Asjad, Muhammad Imran, Faridi, Waqas Ali, Jhangeer, Adil, Aleem, Maryam, Yusuf, Abdullahi, Alshomrani, Ali S., Baleanu, Dumitru, and Mühendislik ve Doğa Bilimleri Fakültesi

Subjects
Fractional Derivatives, New Extended Direct Algebraic Method, Travelling Wave Transformation, General Mathematics, Multi-Wave Non-Linear Hirota Equation, Soliton Solutions
Abstract

The aim of study is to investigate the Hirota equation which has a significant role in applied sciences, like maritime, coastal engineering, ocean, and the main source of the environmental action due to energy transportation on floating anatomical structures. The classical Hirota model has transformed into a fractional Hirota governing equation by using the space-time fractional Riemann-Liouville, time fractional Atangana-Baleanu and space-time fractional $ \beta $ differential operators. The most generalized new extended direct algebraic technique is applied to obtain the solitonic patterns. The utilized scheme provided a generalized class of analytical solutions, which is presented by the trigonometric, rational, exponential and hyperbolic functions. The analytical solutions which cover almost all types of soliton are obtained with Riemann-Liouville, Atangana-Baleanu and $ \beta $ fractional operator. The influence of the fractional-order parameter on the acquired solitary wave solutions is graphically studied. The two and three-dimensional graphical comparison between Riemann-Liouville, Atangana-Baleanu and $ \beta $-fractional derivatives for the solutions of the Hirota equation is displayed by considering suitable involved parametric values with the aid of Mathematica.

Published
2022

35. Mellin transform for fractional integrals with general analytic kernel

Author

Rashid, Maliha, Kalsoom, Amna, Sager, Maria, İnç, Mustafa, Baleanu, Dumitru, Alshomrani, Ali S., and Mühendislik ve Doğa Bilimleri Fakültesi

Subjects
Fractional Integrals, Caputo Fractional Derivative, Mellin Transform, Laplace and Fourier Transforms
Abstract

Many different operators of fractional calculus have been proposed, which can be organized in some general classes of operators. According to this study, the class of fractional integrals and derivatives can be classified into two main categories, that is, with and without general analytical kernel (introduced in 2019). In this article, we define the Mellin transform for fractional differential operator with general analytic kernel in both Riemann-Liouville and Caputo derivatives of order ς ≥ 0 and ϱ be a fixed parameter. We will also establish relation between Mellin transform with Laplace and Fourier transforms.

Published
2022

36. On the breather waves, lump solutions, two-wave solutions of (3+1) dimensional Martínez Alonso–Shabat equation

Author

Yusuf, Abdullahi, Alshomrani, Ali S., Sulaiman, Tukur Abdulkadir, Younas, Usman, Baleanu, Dumitru, and Mühendislik ve Doğa Bilimleri Fakültesi

Subjects
Hirota's Bilinear Method, Multi-Waves, Lump Solution, Breather Waves, Martínez Alonso–Shabat Equation
Abstract

We effectively utilize Hirota’s bilinear method (HBM) in this article to scrutinize the diverse wave profiles to the (3 + 1) dimensional Martínez Alonso–Shabat equation when the test function approaches are taken into consideration. Several novel breather waves, lump solutions, and two-wave solutions are obtained. Furthermore, with the assistance of appropriate parameters, the reported results’ physical behavior is sketched out in several 3 dimensional, 2 dimensional, and contour profiles. The obtained results are useful in grasping the fundamental scenarios of nonlinear sciences as well as the related nonlinear higher dimensional wave fields, both of which are important. With the help of Mathematica, the obtained results are verified by inserting them into the governing equation. Thus, our programmes, which are based on the fortress of representative calculations, provide a robust mathematical framework for resolving difficult nonlinear wave problems.

Published
2022

49. THERMAL ANALYSIS OF MAGNETOHYDRODYNAMIC VISCOUS FLUID WITH INNOVATIVE FRACTIONAL DERIVATIVE.

Author

AHMAD, Mushtaq, IMRAN, Muhammad Asjad, BALEANU, Dumitru, and ALSHOMRANI, Ali S.

Subjects
THERMAL analysis, CAPUTO fractional derivatives, FLUIDS, HEAT transfer
Abstract

In this study, an attempt is made to investigate a fractional model of unsteady and an incompressible MHD viscous fluid with heat transfer. The fluid is lying over a vertical and moving plate in its own plane. The problem is modeled by using the constant proportional Caputo fractional derivatives with suitable boundary conditions. The non-dimensional governing equations of problem have been solved analytically with the help of Laplace transform techniques and explicit expressions for respective field variable are obtained. The transformed solutions for energy and momentum balances are appeared in terms of series form. The analytical results regarding velocity and temperature are plotted graphically by MATHCAD software to see the influence of physical parameters. Some graphic comparisons are also mad among present results with hybrid fractional derivatives and the published results that have been obtained by Caputo. It is found that the velocity and temperature with constant proportional Caputo fractional derivative are portrait better decay than velocities and temperatures that obtained with Caputo and Caputo-Fabrizio derivative. Further, rate of heat transfer and skin friction can be enhanced with smaller values of fractional parameter. [ABSTRACT FROM AUTHOR]

Published
2020
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50. NEW ANALYTICAL SOLUTIONS OF HEAT TRANSFER FLOW OF CLAY-WATER BASE NANOPARTICLES WITH THE APPLICATION OF NOVEL HYBRID FRACTIONAL DERIVATIVE.

Author

ASJAD, Muhammad Imran, IKRAM, Muhammad Danish, ALI, Rizwan, BALEANU, Dumitru, and ALSHOMRANI, Ali S.

Subjects
ANALYTICAL solutions, NANOFLUIDS, HEAT transfer, THERMOPHYSICAL properties, FORCED convection, DIESEL motors, FREE convection
Abstract

Clay nanoparticles are hanging in three different based fluids (water, kerosene, and engine oil). The exact terminologies of Maxwell-Garnett and Brinkman for the current thermophysical properties of clay nanofluids are used, while the flow occurrence is directed by a set linear PDE with physical initial and boundary conditions. The classical governing equations are extended to non-integer order hybrid fractional derivative which is introduced in [33]. Analytical solutions for temperature and velocity fields are attained via Laplace transform technique. Some limiting solutions are also obtained from the existing literature and compared for different values of fractional parameter. To vision the impact of several flow parameters on the temperature and velocity some graphs are drawn using Mathcad software and designed in different figures. As a result, we found that hybrid fractional model is better in describing the decay behavior of temperature and velocity in comparison of classical derivatives. In comparison of nanofluid with different base fluids, it is concluded that water-based nanofluid has higher velocity than others. [ABSTRACT FROM AUTHOR]

Published
2020
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