Browsing by Author "Al-Mdallal, Qasem M."

Now showing 1 - 9 of 9

Citation Count: Laadjal, Zaid; Al-Mdallal, Qasem M.; Jarad, Fahd (2021). "Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions", Journal of Mathematics, Vol. 2021.
Analysis of a Coupled System of Nonlinear Fractional Langevin Equations with Certain Nonlocal and Nonseparated Boundary Conditions
(2021) Laadjal, Zaid; Al-Mdallal, Qasem M.; Jarad, Fahd; 234808
In this article, we use some fixed point theorems to discuss the existence and uniqueness of solutions to a coupled system of a nonlinear Langevin differential equation which involves Caputo fractional derivatives of different orders and is governed by new type of nonlocal and nonseparated boundary conditions consisting of fractional integrals and derivatives. The considered boundary conditions are totally dissimilar than the ones already handled in the literature. Additionally, we modify the Adams-type predictor-corrector method by implicitly implementing the Gauss-Seidel method in order to solve some specific particular cases of the system.
Citation Count: Abdeljawad, T...et al. (2020). "Analysis of Some Generalized Abc – Fractional Logistic Models",Analysis of Some Generalized Abc – Fractional Logistic Models.
Analysis of Some Generalized Abc – Fractional Logistic Models
(Elsevier B.V., 2020) Abdeljawad, Thabet; Hajji, Mohamed A.; Al-Mdallal, Qasem M.; Jarad, Fahd; 234808
In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilibrium points. Numerical illustrative examples are discussed for the studied models.
Citation Count: Haq, Fazal...et al. (2019). "Application of a hybrid method for systems of fractional order partial differential equations arising in the model of the one-dimensional Keller-Segel equation", European Physical Journal Plus, Vol. 134, No. 9.
Application of a hybrid method for systems of fractional order partial differential equations arising in the model of the one-dimensional Keller-Segel equation
(Springer Heidelberg, 2019) Haq, Fazal; Shah, Kamal; Al-Mdallal, Qasem M.; Jarad, Fahd; 234808
In this paper, we apply a hybrid method due to coupling the Laplace transform with the Adomian decomposition method (LADM) for solving nonlinear fractional differential equations that appear in the model of Keller-Segel equations with one dimension. We explain the adopted method is with several examples. It turns out that the reliability of LADM and the reductions in computations show that LADM is widely applicable. We also compare our results with the results of homotopy decomposition method (HDM).
Citation Count: Abdeljawad, Thabet; Al-Mdallal, Qasem M.; Jarad, Fahd, "Fractional logistic models in the frame of fractional operators generated by conformable derivatives", Chaos Solitons & Fractals, Vol. 119, pp. 94-101, (2019).
Fractional logistic models in the frame of fractional operators generated by conformable derivatives
(Pergamon-Elsevier Science LTD, 2019) Abdeljawad, Thabet; Al-Mdallal, Qasem M.; Jarad, Fahd; 234808
In this article, we study different types of fractional-order logistic models in the frame of Caputo type fractional operators generated by conformable derivatives (Caputo CFDs). We present the existence and uniqueness theorems to solutions of these models and discuss their stability by perturbing the equilibrium points. Finally, we furniture our results by illustrative numerical examples for the studied models. (C) 2018 Elsevier Ltd. All rights reserved.
Citation Count: Thumma, Thirupathi...et al. "Heat transfer analysis of magnetized Cu-Ag-H2O hybrid nanofluid radiative flow over a spinning disk when the exponential heat source and Hall current are substantial: Optimization and sensitivity analysis", Case Studies in Thermal Engineering, Vol. 50.
Heat transfer analysis of magnetized Cu-Ag-H2O hybrid nanofluid radiative flow over a spinning disk when the exponential heat source and Hall current are substantial: Optimization and sensitivity analysis
(2023) Thumma, Thirupathi; Pyari, Devarsu Radha; Ontela, Surender; Al-Mdallal, Qasem M.; Jarad, Fahd; 234808
The main motive of the instigated mathematical model is to observe the impact of Hall current on the hybrid nanofluid flow over a disk that is rotating. The copper and silver metal nanoparticles have been considered with volume fraction φ1=φ2=0.01(0.01)0.04 and are suspended in water to form the hybrid nanofluid. Diverse characteristics like magnetic field, thermal radiation, and (ESHS) exponential space dependent heat source are incorporated to investigate the nature of the flow. The present mathematical model is initiated with partial derivative equations (PDEs) which are redrafted as ordinary derivative equations (ODEs) with appropriate transformations of similarity. The results are attained through a blend of the Runge-Kutta method, shooting procedure, and the influences of parameters on the flow of nanofluid and hybrid nanofluid are compared and illustrated both as tables and graphs. The present numerical research is unique because by employing a complete quadratic CCD framework using the RSM strategy, the sensitivity and optimization analysis of the heat transmission improvement for the volume fraction, ESHS, and thermal radiation parameters have been performed. The R-squared and adjusted R-Squared are obtained as 100%. The residual graphs and contour diagrams of the same are also shown. The current study establishes that the Hall parameter increases the radial velocity, but it also controls the energy and cross-radial velocity. The rate of heat transmission is increased by thermal radiation even at low levels of ESHS. The rate of heat transmission is more sensitive (0.024670) to the volume fraction of the hybrid nanofluid when ESHS is at an intermediate level. The lowest sensitivity (-1.269967) value towards ESHS is observed For thermal radiation and ESHS parameter values, the heat transmission rate of the mono nanofluid is not as great as that of hybrid nanofluid. The current study finds applications in the generation of hydroelectric power, air cleansing and rotating equipment, healthcare devices, and many other industries.
Citation Count: Baba, Isa Abdullahi;...et.al. (2022). "Numerical And Theoretical Analysis Of An Awareness Covid-19 Epidemic Model Via Generalized Atangana-Baleanu Fractional Derivative", Journal of Applied Mathematics and Computational Mechanics, Vol.21, No.1, pp.7-18.
Numerical And Theoretical Analysis Of An Awareness Covid-19 Epidemic Model Via Generalized Atangana-Baleanu Fractional Derivative
(2022) Baba, Isa Abdullahi; Ahmed, Idris; Al-Mdallal, Qasem M.; Jarad, Fahd; Yunusa, Salisu; 234808
In this paper, a COVID-19 Awareness model in the setting of a generalized fractional Atangana-Baleanu derivative is proposed. The existence and uniqueness of a solution of the proposed fractional-order model are investigated under the techniques of fixed point theorems. In addition, we perform the predictor-corrector method to find its numeric solutions and present the graphs of the various solutions using different values of the parameters embodied in the derivative.
Citation Count: Alomari, Abedel-Karrem...et al. (2020). "Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels", Numerical Methods for Partial Differential Equations.
Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels
(2020) Alomari, Abedel-Karrem; Abdeljawad, Thabet; Baleanu, Dumitru; Saad, Khaled M.; Al-Mdallal, Qasem M.; 56389
In this article, we investigate the generalized fractional operator Caputo type (ABC) with kernels of Mittag–Lefller in three parameters Eα,µγ(λ,t) and its fractional integrals with arbitrary order for solving the time fractional parabolic nonlinear equation. The generalized definition generates infinitely many problems for a fixed fractional derivative α. We utilize this operator with homotopy analysis method for constructing the new scheme for generating successive approximations. This procedure is used successfully on two examples for finding the solutions. The effectiveness and accuracy are verified by clarifying the convergence region in the ℏ-curves as well as by calculating the residual error and the results were accurate. Based on the experiment, we verify the existence of the solution for the new parameters. Depending on these results, this treatment can be used to find approximate solutions to many fractional differential equations.
Citation Count: Al Fahel, Sara;...et.al. (2023). "Quadratic and cubic logistic models involving Caputo-Fabrizio operator", European Physical Journal - Special Topics, Vol.232, No.14-15, pp.2351-2355.
Quadratic and cubic logistic models involving Caputo-Fabrizio operator
(2023) Al Fahel, Sara; Baleanu, Dumitru; Al-Mdallal, Qasem M.; Saad, Khaled M.; 56389
In this paper, we numerically investigate the fractional quadratic and cubic logistic models involving the Caputo-Fabrizio operator. We construct the successive iterations using the theory of fractional calculus and Lagrange polynomials. Then, we handled the exact solutions of these models. The validity of the accuracy and efficiency will be satisfied through some numerical results.
Citation Count: Derbazi, Choukri...et al. "Some qualitative properties of solutions to a nonlinear fractional differential equation involving two Φ-Caputo fractional derivatives", AIMS Mathematics, Vol. 7, no. 6, pp. 9894-9910.
Some qualitative properties of solutions to a nonlinear fractional differential equation involving two Φ-Caputo fractional derivatives
(2022) Derbazi, Choukri; Al-Mdallal, Qasem M.; Jarad, Fahd; Baitiche, Zidane; 234808
The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate of the solutions, the continuous dependence of the solutions on initial conditions and the existence and uniqueness of extremal solutions to a new class of fractional differential equations involving two fractional derivatives in the sense of Caputo fractional derivative with respect to another function Φ. Firstly, using the generalized Laplace transform method, we give an explicit formula of the solutions to the aforementioned linear problem which can be regarded as a novelty item. Secondly, by the implementation of the Φ-fractional Gronwall inequality, we analyze some properties such as estimates and continuous dependence of the solutions on initial conditions. Thirdly, with the help of features of the Mittag-Leffler functions (MLFs), we build a new comparison principle for the corresponding linear equation. This outcome plays a vital role in the forthcoming analysis of this paper especially when we combine it with the monotone iterative technique alongside facet with the method of upper and lower solutions to get the extremal solutions for the analyzed problem. Lastly, we present some examples to support the validity of our main results. © 2022 the Author(s), licensee AIMS Press.