Browsing by Author "Farooq, Umar"

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Citation Count: Shah, Rasool...et al. (2019). "A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations", IEEE Access, Vol. 7.
A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations
(IEEE-INST Electrical Electronics Engineers INC, 2019) Shah, Rasool; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; 56389
In this research article, a new analytical technique is implemented to solve system of fractional-order partial differential equations. The fractional derivatives are carried out with the help of Caputo fractional derivative operator. The direct implementation of Mohand and its inverse transformation provide sufficient easy less and reliability of the proposed method. Decomposition method along with Mohand transformation is proceeded to attain the analytical solution of the targeted problems. The applicability of the suggested method is analyzed through illustrative examples. The solutions graph has the best contact with the graphs of exact solutions in paper. Moreover, the convergence of the present technique is sufficiently fast, so that it can be considered the best technique to solve system of nonlinear fractional-order partial differential equations.
Citation Count: Ali, I...et al. (2012). "An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations", IEEE Access, Vol. 8, pp. 25638-25649.
An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations
(Institute of Electrical and Electronics Engineers Inc., 2020) Ali, Izaz; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Arif, Muhammad; 56389
In the present research article, a modified analytical method is applied to solve time-fractional telegraph equations. The Caputo-operator is used to express the derivative of fractional-order. The present method is the combination of two well-known methods namely Mohan transformation method and Adomian decomposition method. The validity of the proposed technique is confirmed through illustrative examples. It is observed that the obtained solutions have strong contact with the exact solution of the examples. Moreover, it is investigated that the present method has the desired degree of accuracy and provided the graphs closed form solutions of all targeted examples. The graphs have verified the convergence analysis of fractional-order solutions to integer-order solution. In conclusion, the suggested method is simple, straightforward and an effective technique to solve fractional-order partial differential equations.
Citation Count: Khan, H...et al. (2020). ,"Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method",Applied Sciences (Switzerland), Vol. 10. No. 1.
Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method
(MDPI AG, 2020) Khan, Hassan; Farooq, Umar; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
In this article, a new analytical technique based on an innovative transformation is used to solve (2+time fractional-order) dimensional physical models. The proposed method is the hybrid methodology of Shehu transformation along with Adomian decomposition method. The series form solution is obtained by using the suggested method which provides the desired rate of convergence. Some numerical examples are solved by using the proposed method. The solutions of the targeted problems are represented by graphs which have confirmed closed contact between the exact and obtained solutions of the problems. Based on the novelty and straightforward implementation of the method, it is considered to be one of the best analytical techniques to solve linear and non-linear fractional partial differential equations.
Citation Count: Shah, Rasool...et al. (2020). "Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique", Frontiers in Physics, Vol. 7.
Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique
(2020) Shah, Rasool; Farooq, Umar; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
In the present article, fractional view of third order Kortewege-De Vries equations is presented by a sophisticated analytical technique called Mohand decomposition method. The Caputo fractional derivative operator is used to express fractional derivatives, containing in the targeted problems. Some numerical examples are presented to show the effectiveness of the method for both fractional and integer order problems. From the table, it is investigated that the proposed method has the same rate of convergence as compare to homotopy perturbation transform method. The solution graphs have confirmed the best agreement with the exact solutions of the problems and also revealed that if the sequence of fractional-orders is approaches to integer order, then the fractional order solutions of the problems are converge to an integer order solution. Moreover, the proposed method is straight forward and easy to implement and therefore can be used for other non-linear fractional-order partial differential equations.
Citation Count: Farooq, Umar...et al. (2021). "New approximate analytical technique for the solution of time fractional fluid flow models", Advances in Difference Equations, Vol. 2021, No. 1.
New approximate analytical technique for the solution of time fractional fluid flow models
(2021) Farooq, Umar; Khan, Hassan; Tchier, Fairouz; Hınçal, Evren; Baleanu, Dumitru; Bin Jebreen, Haifa; 56389
In this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier–Stokes model. The approximate analytical solution is obtained within Liouville–Caputo operator. The analytical strategy generates the series form solution, with less computational work and fast convergence rate to the exact solutions. The obtained results have shown a simple and useful procedure to analyze complex problems in related areas of science and technology. © 2021, The Author(s).
Citation Count: Farooq, Umar;...et.al. (2023). "Numerical framework of hybrid nanofluid over two horizontal parallel plates with non-linear thermal radiation", International Journal of Thermofluids, Vol.18.
Numerical framework of hybrid nanofluid over two horizontal parallel plates with non-linear thermal radiation
(2023) Farooq, Umar; Waqas, Hassan; Noreen, Sobia; Imran, Muhammad; Akgül, Ali; Baleanu, Dumitru; Din, Sayed M.El; Muhammad, Taseer; Galal, Ahmed M; 56389
Significance of study: High combustion temperatures necessitate appropriate cooling systems in the combustion process. Regenerative cooling is used in the majority of chambers in liquid propellant engines. The addition of nanoparticles to the cooling fluid is a novel technique to increase the efficiency of heat transfer in the regenerative cooling process. Aim of the study: In this investigation, we investigate the two-dimensional flow of the hybrid nanofluid with suction/injection effect over two horizontal parallel plates. The non-linear thermal radiation effect is measured in the model of a hybrid nanofluid. Here we use single-walled carbon nanotubes, multi-walled carbon nanotubes, nickel-zinc iron oxide, and manganese zinc iron oxide with base fluid engine oil. The effects of different shape factors (Sphere, Bricks, Cylinder, Platelets, Column, and Lamina)are also incorporated. Research methodology: Using appropriate similarity transformations, the controlling partial differential equations are transformed into ordinary differential equations. Using the shooting strategy, the transformed higher-order ordinary differential equations are converted to first-order ordinary differential equations, and the Bvp4c built-in function in MATLAB is used to produce the numerical and graphical results of the flow parameter. Conclusion: The velocity profile is decreased by the increasing values of the suction/injection parameter. The temperature distribution profile declined for the higher values of the temperature ratio parameter. The combination of nickel zinc iron oxide and carbon nanotube nanomaterials to engine oil as a cooling fluid enhanced the heat transfer coefficient. According to the findings, carbon nanotubes outperform nickel zinc iron oxide nanoparticles in terms of increasing heat transfer coefficient and improving regenerative cooling.
Citation Count: Alharbi, Khalid Abdulkhaliq M.;...et.al. (2023). "Numerical solution of Maxwell-Sutterby nanofluid flow inside a stretching sheet with thermal radiation, exponential heat source/sink, and bioconvection", International Journal of Thermofluids, Vol.18.
Numerical solution of Maxwell-Sutterby nanofluid flow inside a stretching sheet with thermal radiation, exponential heat source/sink, and bioconvection
(2023) Alharbi, Khalid Abdulkhaliq M.; Farooq, Umar; Waqas, Hassan; Imran, Muhammad; Noreen, Sobia; Akgül, Ali; Baleanu, Dumitru; Din, Sayed M.El; Abbas, Khizer; 56389
A Survey of literature illustrates that nano liquid is further helpful for heat transportation as compared to regular liquid. Nonetheless, there are considerable gaps in our understanding of existing approaches for enhancing heat transmission in nanofluids, necessitating comprehensive research of these fluids. The current approach proposes to investigate the influence of a Maxwell-Sutterby nanofluid on a sheet while accounting for heat radiation. This paper investigates activation energy, and exponential heat source/sink. Bioconvection and motile microorganisms with Brownian motion and thermophoresis effects are considered.y linked similarity transformations, the boundary layer set of controlling partial differential equations are transformed into ordinary differential equations. A numerical strategy (shooting technique) is used to handle the transformed system of ordinary differential equations through the Bvp4c solver of the computing tool MATLAB. The results for velocity and temperature, concentration, and motile microbe profiles are numerically and graphically examined for various parameters. The velocity distribution profile decreased as the magnetic parameter varied, but increased when the mixed convection parameter increased in magnitude. The heat flux profile is improved with higher estimations of the Biot number and thermophoresis parameter. When the Prandtl number and the Brownian motion parameter's values rise, the energy profile falls. When the Peclet number and bioconvection Lewis number increased, the profile of mobile microorganisms dropped.
Citation Count: Farooq, Umar...et al. (2019). "Numerical solutions of fractional delay differential equations using Chebyshev wavelet method", Computational & Applied Mathematics, Vol. 38, No. 4.
Numerical solutions of fractional delay differential equations using Chebyshev wavelet method
(Springer Heidelberg, 2019) Farooq, Umar; Khan, Hassan; Baleanu, Dumitru; Arif, Muhammad; 56389
In the present research article, we used a new numerical technique called Chebyshev wavelet method for the numerical solutions of fractional delay differential equations. The Caputo operator is used to define fractional derivatives. The numerical results illustrate the accuracy and reliability of the proposed method. Some numerical examples presented which have shown that the computational study completely supports the compatibility of the suggested method. Similarly, a proposed algorithm can also be applied for other physical problems.