Yazar "Nadeem, Muhammad" seçeneğine göre listele

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    A Computational Scheme for the Numerical Results of Time-Fractional Degasperis-Procesi and Camassa-Holm Models
    (Mdpi, 2022) Nadeem, Muhammad; Jafari, Hossein; Akgul, Ali; De la Sen, Manuel
    This article presents an idea of a new approach for the solitary wave solution of the modified Degasperis-Procesi (mDP) and modified Camassa-Holm (mCH) models with a time-fractional derivative. We combine Laplace transform (LT) and homotopy perturbation method (HPM) to formulate the idea of the Laplace transform homotopy perturbation method (LHPTM). This study is considered under the Caputo sense. This proposed strategy does not depend on any assumption and restriction of variables, such as in the classical perturbation method. Some numerical examples are demonstrated and their results are compared graphically in 2D and 3D distribution. This approach presents the iterations in the form of a series solutions. We also compute the absolute error to show the effective performance of this proposed scheme.
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    A Novel Approach for the Approximate Solution of Wave Problems in Multi-Dimensional Orders with Computational Applications
    (Mdpi, 2022) Nadeem, Muhammad; Akguel, Ali; Guran, Liliana; Bota, Monica-Felicia
    The main goal of this paper is to introduce a new scheme, known as the Aboodh homotopy integral transform method (AHITM), for the approximate solution of wave problems in multi-dimensional orders. The Aboodh integral transform (AIT) removes the restriction of variables in the recurrence relation, whereas the homotopy perturbation method (HPM) derives the successive iterations using the initial conditions. The convergence analysis is provided to study a wave equation with multiple dimensions. Some computational applications are considered to show the efficiency of this scheme. Graphical representation between the approximate and the exact solution predicts the high rate of convergence of this approach.
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    Analysis of fuzzified boundary value problems for MHD Couette and Poiseuille flow
    (Nature Portfolio, 2022) Siddique, Imran; Nadeem, Muhammad; Khan, Ilyas; Jamil, Raja Noshad; Shamseldin, Mohamed A.; Akgul, Ali
    In an uncertain atmosphere, the magnetohydrodynamics (MHD) flow in three principal flows of the third grade fluid across two parallel plates is presented. Fuzzy differential equations are constructed by manipulating dimensionless differential equations. The prime purpose of the current article is to use a semi-analytical approach fuzzy-based Adomian decomposition method to achieve numerical results for nonlinear FDEs with fuzzy boundary conditions. Triangular fuzzy numbers are used in fuzzy BCs with help of alpha-cut approach. This strategy is linked to the membership function. In a graphic and tabular depiction, the effect of a and other constraints on fuzzy velocity profiles is explored. The current findings are in good agreement with their previous numerical and analytical results in a crisp environment.
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    Approximate Solution of Nonlinear Time-Fractional Klein-Gordon Equations Using Yang Transform
    (Mdpi, 2022) Liu, Jinxing; Nadeem, Muhammad; Habib, Mustafa; Akgul, Ali
    The algebras of the symmetry operators for the Klein-Gordon equation are important for a charged test particle, moving in an external electromagnetic field in a space time manifold on the isotropic hydrosulphate. In this paper, we develop an analytical and numerical approach for providing the solution to a class of linear and nonlinear fractional Klein-Gordon equations arising in classical relativistic and quantum mechanics. We study the Yang homotopy perturbation transform method (YHPTM),which is associated with the Yang transform (YT) and the homotopy perturbation method (HPM), where the fractional derivative is taken in a Caputo-Fabrizio (CF) sense. This technique provides the solution very accurately and efficiently in the form of a series with easily computable coefficients. The behavior of the approximate series solution for different fractional-order p values has been shown graphically. Our numerical investigations indicate that YHPTM is a simple and powerful mathematical tool to deal with the complexity of such problems.
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    Bifurcation Analysis of Travelling Waves and Multi-rogue Wave Solutions for a Nonlinear Pseudo-Parabolic Model of Visco-Elastic Kelvin-Voigt Fluid
    (Hindawi Ltd, 2022) Uddin, Sabur; Karim, Shazia; Alshammari, F. S.; Roshid, Harun-Or; Noor, N. F. M.; Hoque, Fazlul; Nadeem, Muhammad
    Through this article, we focus on the extension of travelling wave solutions for a prevalent nonlinear pseudo-parabolic physical Oskolkov model for Kevin-Voigt fluids by using two integral techniques. First of all, we explore the bifurcation and phase portraits of the model for different parametric conditions via a dynamical system approach. We derive smooth waves of the bright bell and dark bell, periodic waves, and singular waves of dark and bright cusps, in correspondence to homoclinic, periodic, and open orbits with cusp, respectively. Each orbit of the phase portraits is envisaged through various energy states. Secondly, with the help of a prevalent unified scheme, an inventive version of exact analytic solutions comprising hyperbolic, trigonometric, and rational functions can be invented with some collective parameters. The unified scheme is an excitably auspicious method to procure novel interacting travelling wave solutions and to obtain multipeaked bright and dark solitons, shock waves, bright bell waves with single and double shocks, combo waves of the bright-dark bell and dark-bright bell with a shock, dark bell into a double shock wave, and bright-dark multirogue type wave solutions of the model. The dynamics of the procured nonlinear wave solutions are also presented through 2-D, 3-D, and density plots with specified parameters.
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    Controllability of Impulsive Neutral Fractional Stochastic Systems
    (Mdpi, 2022) Ain, Qura Tul; Nadeem, Muhammad; Akgul, Ali; De la Sen, Manuel
    The study of dynamic systems appears in various aspects of dynamical structures such as decomposition, decoupling, observability, and controllability. In the present research, we study the controllability of fractional stochastic systems (FSF) and examine the Poisson jumps in finite dimensional space where the fractional impulsive neutral stochastic system is controllable. Sufficient conditions are demonstrated with the aid of fixed point theory. The Mittag-Leffler (ML) matrix function defines the controllability of the Grammian matrix (GM). The relation to symmetry is clear since the controllability Grammian is a hermitian matrix (since the integrand in its definition is hermitian) and this is the complex version of a symmetric matrix. In fact, such a Grammian becomes a symmetric matrix in the specific scenario where the controllability Grammian is a real matrix. Some examples are provided to demonstrate the feasibility of the present theory.
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    Numerical Investigation of Nonlinear Shock Wave Equations with Fractional Order in Propagating Disturbance
    (Mdpi, 2022) Fang, Jiahua; Nadeem, Muhammad; Habib, Mustafa; Akgul, Ali
    The symmetry design of the system contains integer partial differential equations and fractional-order partial differential equations with fractional derivative. In this paper, we develop a scheme to examine fractional-order shock wave equations and wave equations occurring in the motion of gases in the Caputo sense. This scheme is formulated using the Mohand transform (MT) and the homotopy perturbation method (HPM), altogether called Mohand homotopy perturbation transform (MHPT). Our main finding in this paper is the handling of the recurrence relation that produces the series solutions after only a few iterations. This approach presents the approximate and precise solutions in the form of convergent results with certain countable elements, without any discretization or slight perturbation theory. The numerical findings and solution graphs attained using the MHPT confirm that this approach is significant and reliable.
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    Optimal variational iteration method for parametric boundary value problem
    (Amer Inst Mathematical Sciences-Aims, 2022) Ain, Qura Tul; Nadeem, Muhammad; Karim, Shazia; Akguel, Ali; Jarad, Fahd
    Mathematical applications in engineering have a long history. One of the most well-known analytical techniques, the optimal variational iteration method (OVIM), is utilized to construct a quick and accurate algorithm for a special fourth-order ordinary initial value problem. Many researchers have discussed the problem involving a parameter c. We solve the parametric boundary value problem that can't be addressed using conventional analytical methods for greater values of c using a new method and a convergence control parameter h. We achieve a convergent solution no matter how huge c is. For the approximation of the convergence control parameter h, two strategies have been discussed. The advantages of one technique over another have been demonstrated. Optimal variational iteration method can be seen as an effective technique to solve parametric boundary value problem.
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    Processed Manures with Added Zinc Improve Zinc Biofortification in Lentils under Saline Conditions
    (Mdpi, 2024) Younas, Noman; Naveed, Muhammad; Yaseen, Muhammad; Younas, Madeeha; Mumtaz, Muhammad Zahid; Babar, Muhammad Hussnain; Nadeem, Muhammad
    The low solubility and enhanced fixation of zinc (Zn) in semi-arid and dry climates limits Zn uptake in plants. Zn deficiency in soil impairs crop production and human health, necessitating agricultural biofortification. A pot experiment was conducted to evaluate the effect of Zn and various types of manure on the Zn biofortification of lentils. The treatments, consisting of a control (Con), normal manure (NM), composted manure (CM), and acidified manure (AM), were applied under saline soil (EC 8.00 dS m-1) and non-saline soil (EC 1.48 dS m-1) conditions along with two levels of Zn, including Zn at 0 kg ha-1 (native soil Zn = 2.2 mg kg-1) and Zn at 25 kg ha-1 (62.2 mg Zn kg-1 soil was achieved). The AM was prepared by adding sulfur and sulfur-oxidizing bacteria to the composted manure. All the manures were applied at 1% (w/w), and ZnSO4 (33% Zn) was used as a Zn source. Lentil variety Masoor 2021 was cultivated as a test crop in five replications of each treatment arranged in a completely randomized design. Applying AM with Zn considerably increased the lentils' growth, yield, and Zn content under saline and non-saline conditions. Under non-saline soils, the treatment of AM + Zn significantly promoted the Zn content in the root (132.5%), shoot (91.7%), grain (49.1%), root length (79.7%), plant height (33.7%), and SPAD value (29.9%). Under saline conditions, application of AM + Zn promoted uptake of Zn in the root (218.5%), Zn content in the shoot (175.7%), Zn accumulation in the grain (107.7%), root length (109.7%), plant height (37.8%), and SPAD value (52.8%) compared to the control. According to the results, lentils should be grown with AM and Zn to increase their growth, yield, and Zn content significantly. This is a cost-effective and sustainable way to combat Zn deficiency in lentils.