Browsing by Author "Farooq, Umar"

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Citation - WoS: 31
Citation - Scopus: 33
A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations
(Ieee-inst Electrical Electronics Engineers inc, 2019) Shah, Rasool; Baleanu, Dumitru; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389; Matematik
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 - WoS: 3
Citation - Scopus: 7
An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations
(Ieee-inst Electrical Electronics Engineers inc, 2020) Ali, Izaz; Baleanu, Dumitru; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389; Matematik
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 - WoS: 34
Citation - Scopus: 41
Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method
(Mdpi, 2020) Khan, Hassan; Baleanu, Dumitru; Farooq, Umar; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389; Matematik
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 - WoS: 27
Citation - Scopus: 36
Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique
(Frontiers Media Sa, 2020) Shah, Rasool; Baleanu, Dumitru; Farooq, Umar; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389; Matematik
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 - WoS: 15
Citation - Scopus: 18
New approximate analytical technique for the solution of time fractional fluid flow models
(Springer, 2021) Farooq, Umar; Baleanu, Dumitru; Khan, Hassan; Tchier, Fairouz; Hincal, Evren; Baleanu, Dumitru; Bin Jebreen, Haifa; 56389; Matematik
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.
Citation - WoS: 14
Citation - Scopus: 18
Numerical solutions of fractional delay differential equations using Chebyshev wavelet method
(Springer Heidelberg, 2019) Farooq, Umar; Baleanu, Dumitru; Khan, Hassan; Baleanu, Dumitru; Arif, Muhammad; 56389; Matematik
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.