Browsing by Author "Ali, Izaz"

Now showing 1 - 4 of 4

An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations
(Institute of Electrical and Electronics Engineers Inc., 2020) Baleanu, Dumitru; 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.
An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems
(2020) Baleanu, Dumitru; Khan, Adnan; Ali, Izaz; Al Qurashi, Maysaa; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; 56389
Mostly, it is very difficult to obtained the exact solution of fractional-order partial differential equations. However, semi-analytical or numerical methods are considered to be an alternative to handle the solutions of such complicated problems. To extend this idea, we used semi-analytical procedures which are mixtures of Laplace transform, Shehu transform and Homotopy perturbation techniques to solve certain systems with Caputo derivative differential equations. The effectiveness of the present technique is justified by taking some examples. The graphical representation of the obtained results have confirmed the significant association between the actual and derived solutions. It is also shown that the suggested method provides a higher rate of convergence with a very small number of calculations. The problems with derivatives of fractional-order are also solved by using the present method. The convergence behavior of the fractional-order solutions to an integer-order solution is observed. The convergence phenomena described a very broad concept of the physical problems. Due to simple and useful implementation, the current methods can be used to solve problems containing the derivative of a fractional-order.
Approximate analytical fractional view of convection-diffusion equations
(2020) Baleanu, Dumitru; Mustafa, Saima; Ali, Izaz; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
In this article, a modified variational iteration method along with Laplace transformation is used for obtaining the solution of fractional-order nonlinear convection-diffusion equations (CDEs). The proposed technique is applied for the first time to solve fractional-order nonlinear CDEs and attain a series-form solution with the quick rate of convergence. Tabular and graphical representations are presented to confirm the reliability of the suggested technique. The solutions are calculated for fractional as well as for integer orders of the problems. The solution graphs of the solutions at various fractional derivatives are plotted. The accuracy is measured in terms of absolute error. The higher degree of accuracy is observed from the table and figures. It is further investigated that fractional solutions have the convergence behavior toward the solution at integer order. The applicability of the present technique is verified by illustrative examples. The simple and effective procedure of the current technique supports its implementation to solve other nonlinear fractional problems in different areas of applied science.
Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations
(2020) Baleanu, Dumitru; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations.