Browsing Matematik Bölümü by Author "Khan, Hassan"

Now showing items 1-20 of 28

A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations

Shah, Rasool; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Kumam, Poom (IEEE-INST Electrical Electronics Engineers INC, 2019)

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 ...
A Novel Method for the Analytical Solution of Fractional Zakharov–Kuznetsov Equations

Shah, Rasool; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad (Springer, 2019-12)

In this article, an efficient analytical technique, called Laplace–Adomian decomposition method, is used to obtain the solution of fractional Zakharov– Kuznetsov equations. The fractional derivatives are described in terms ...
A semi-analytical method to solve family of Kuramoto-Sivashinsky equations

Shah, Rasool; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad (2020-01-01)

In this article, a semi-analytical technique is implemented to solve Kuramoto-Sivashinsky equations. The present method is the combination of two well-known methods namely Laplace transform method and variational iteration ...
An Analytical Investigation of Fractional-Order Biological Model Using an Innovative Technique

Khan, Hassan; Khan, Adnan; Al Qurashi, Maysaa; Baleanu, Dumitru; Shah, Rasool (2020-04-15)

In this paper, a new so-called iterative Laplace transform method is implemented to investigate the solution of certain important population models of noninteger order. The iterative procedure is combined effectively with ...
An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method

Hajira; Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad (2020-12-01)

In this article, a hybrid technique of Elzaki transformation and decomposition method is used to solve the Navier–Stokes equations with a Caputo fractional derivative. The numerical simulations and examples are presented ...
An Approximate-Analytical Solution to Analyze Fractional View of Telegraph Equations

Ali, Izaz; Khan, Hassan; Farooq, Umar; Baleanu, Dumitru; Arif, Muhammad (Institute of Electrical and Electronics Engineers Inc., 2020)

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 ...
An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems

Qin, Ya; Khan, Adnan; Ali, Izaz; Al Qurashi, Maysaa; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru (2020-06)

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 ...
An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations

Khan, Hassan; Shah, Rasool; Kumam, Poom; Arif, Muhammad; Baleanu, Dumitru (MDPI, 2019-05)

In the present article, fractional-order telegraph equations are solved by using the Laplace-Adomian decomposition method. The Caputo operator is used to define the fractional derivative. Series form solutions are obtained ...
Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method

Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad (MDPI, 2019-09)

In the current paper, fractional-order hyperbolic telegraph equations are considered for analytical solutions, using the decomposition method based on natural transformation. The fractional derivative is defined by the ...
Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method

Khan, Hassan; Farooq, Umar; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad (MDPI AG, 2020-01-01)

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 ...
Approximate analytical fractional view of convection-diffusion equations

Khan, Hassan; Mustafa, Saima; Ali, Izaz; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad (2020-01)

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 ...
Exact solutions of the Laplace fractional boundary value problems via natural decomposition method

Hajira; Khan, Hassan; Chu, Yu-Ming; Shah, Rasool; Baleanu, Dumitru; Arif, Muhammad (2020-01-01)

In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural ...
Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations

Ali, Izaz; Khan, Hassan; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad (2020-01)

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 ...
Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique

Shah, Rasool; Farooq, Umar; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad (2020-01-17)

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 ...
Fractional Whitham-Broer-Kaup Equations within Modified Analytical Approaches

Shah, Rasool; Khan, Hassan; Baleanu, Dumitru (2019-12)

The fractional traveling wave solution of important Whitham-Broer-Kaup equations was investigated by using the q-homotopy analysis transform method and natural decomposition method. The Caputo definition of fractional ...
Fractional-Order Investigation of Diffusion Equations via Analytical Approach

Liu, Haobin; Khan, Hassan; Mustafa, Saima; Mou, Lianming; Baleanu, Dumitru (2021-02-23)

This research article is mainly concerned with the analytical solution of diffusion equations within a Caputo fractional-order derivative. The motivation and novelty behind the present work are the application of a ...
Laplace decomposition for solving nonlinear system of fractional order partial differential equations

Khan, Hassan; Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad (2020-07-22)

In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo ...
Laplace decomposition for solving nonlinear system of fractional order partial differential equations

Khan, Hassan; Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad (2020-12-01)

In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo ...
Modified Modelling for Heat Like Equations within Caputo Operator

Khan, Hassan; Khan, Adnan; Al-Qurashi, Maysaa; Shah, Rasool; Baleanu, Dumitru (2020-04)

The present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the ...
Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay

Shah, Rasool; Khan, Hassan; Kumam, Poom; Arif, Muhammad; Baleanu, Dumitru (MDPI, 2019-06)

In the present article, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using Natural transform decomposition method. ...

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