Browsing by Author "Kumam, Poom"

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A Caputo-Fabrizio Fractional-Order Cholera Model And İts Sensitivity Analysis
(2023) Jarad, Fahd; Akgül, Ali; Jarad, Fahd; Kumam, Poom; Nonlaopon, Kamsing; 234808
In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model’s complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters
A New Analytical Technique to Solve System of Fractional-Order Partial Differential Equations
(IEEE-INST Electrical Electronics Engineers INC, 2019) Baleanu, Dumitru; 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.
A Novel Method for the Analytical Solution of Fractional Zakharov–Kuznetsov Equations
(Springer, 2019) Baleanu, Dumitru; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
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 of Caputo sense. The solution of the suggested technique is represented in a series form of Adomian components, which is convergent to the exact solution of the given problems. Furthermore, the results of the present method have shown close relations with the exact approaches of the investigated problems. Illustrative examples are discussed, showing the validity of the current method. The attractive and straightforward procedure of the present method suggests that this method can easily be extended for the solutions of other nonlinear fractional-order partial differential equations. © 2019, The Author(s).
A semi-analytical method to solve family of Kuramoto-Sivashinsky equations
(2020) Baleanu, Dumitru; Khan, Hassan; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
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 method. This hybrid property of the proposed method reduces the numbers of calculations and materials. The accuracy and applicability of the suggested method is confirmed through illustration examples. The accuracy of the proposed method is described in terms of absolute error. It is investigated through graphs and tables that the Laplace transformation and variational iteration method (LVIM) solutions are in good agreement with the exact solution of the problems. The LVIM solutions are also obtained at different fractional-order of the derivative. It is observed through graphs and tables that the fractional-order solutions are convergent to an integer solution as fractional-orders approaches to an integer-order of the problems. In conclusion, the overall implementation of the present method support the validity of the suggested method. Due to simple, straightforward and accurate implementation, the present method can be extended to other non-linear fractional partial differential equations.
An approximate analytical solution of the Navier–Stokes equations within Caputo operator and Elzaki transform decomposition method
(2020) Baleanu, Dumitru; Khan, Hassan; Khan, Adnan; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
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 to show the validity of the suggested method. The solutions are determined for the problems of both fractional and integer orders by a simple and straightforward procedure. The obtained results are shown and explained through graphs and tables. It is observed that the derived results are very close to the actual solutions of the problems. The fractional solutions are of special interest and have a strong relation with the solution at the integer order of the problems. The numerical examples in this paper are nonlinear and thus handle its solutions in a sophisticated manner. It is believed that this work will make it easy to study the nonlinear dynamics, arising in different areas of research and innovation. Therefore, the current method can be extended for the solution of other higher-order nonlinear problems.
An Efficient Analytical Technique, for The Solution of Fractional-Order Telegraph Equations
(MDPI, 2019) Baleanu, Dumitru; Shah, Rasool; Kumam, Poom; Arif, Muhammad; Baleanu, Dumitru; 56389
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 for fractional-order telegraph equations by using the proposed method. Some numerical examples are presented to understand the procedure of the Laplace-Adomian decomposition method. As the Laplace-Adomian decomposition procedure has shown the least volume of calculations and high rate of convergence compared to other analytical techniques, the Laplace-Adomian decomposition method is considered to be one of the best analytical techniques for solving fractional-order, non-linear partial differential equationsparticularly the fractional-order telegraph equation.
An exploration of heat and mass transfer for MHD flow of Brinkman type dusty fluid between fluctuating parallel vertical plates with arbitrary wall shear stress
(2024) Jarad, Fahd; Ali, Gohar; Kumam, Poom; Jarad, Fahd; 234808
An equitably complex phenomenon, the Brinkman-type dusty fluid and wall shear stress effect, is utilized in various engineering and product-making fields. For instance, dusty fluids are employed in nuclear-powered reactors and gas freezing systems to reduce heat of the system. To ascertain the impact of wall shear stress on Brinkman-type dusty fluid flow, the current study intends to do so. Base on this motivation, this paper discusses the two-phase MHD fluctuating flow of a Brinkman-type dusty fluid along with heat and mass transport. Two parallel non-conducting plates are used to model the flow, one at rest and the other in motion. Heat and mass transfer, along with wall share stress, are also taken into consideration, and plate fluctuation allows the flow to occur. The Poincaré-Lighthill fluctuation method was utilised in the process to investigate systematic solutions. The findings were achieved and plotted on a graph. The two-phase flow model is created by independently simulating the fluid and dust particle equations. The effect of relevant aspects such as the Grashof number, magnetic parameter, heat flux, and dusty fluid variable on the base fluid velocity has been explored. It was found that as the magnetic flux and imposed shear force decrease, the velocity of the base fluid increases. Additionally estimated in tabular form are rate of heat transfer and skin friction, two crucial fluid parameters for engineers. According to the graphical analysis, the Brinkman kind dusty fluid has better control over dust particle and fluid velocity rather than viscous fluid. By adjusting the value of N, you may control the temperature profile. Also, by adjusting the value of Sc and γ, you may control the concentration profile.
Analytical Solution of Fractional-Order Hyperbolic Telegraph Equation, Using Natural Transform Decomposition Method
(MDPI, 2019) Baleanu, Dumitru; Shah, Rasool; Baleanu, Dumitru; Kumam, Poom; Arif, Muhammad; 56389
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 Caputo operator. The present technique is implemented for both fractional- and integer-order equations, showing that the current technique is an accurate analytical instrument for the solution of partial differential equations of fractional-order arising in all branches of applied sciences. For this purpose, several examples related to hyperbolic telegraph models are presented to explain the procedure of the suggested method. It is noted that the procedure of the present technique is simple, straightforward, accurate, and found to be a better mathematical technique to solve non-linear fractional partial differential equations.
Analytical Solutions of (2+Time Fractional Order) Dimensional Physical Models, Using Modified Decomposition Method
(MDPI AG, 2020) Baleanu, Dumitru; 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.
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.
Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition
(2020) Abdeljawad, Thabet; Jarad, Fahd; Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; 234808
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained. © 2020, The Author(s).
Existence and uniqueness results for Φ-Caputo implicit fractional pantograph differential equation with generalized anti-periodic boundary condition
(2020) Abdeljawad, Thabet; Jarad, Fahd; Abdeljawad, Thabet; Jarad, Fahd; Borisut, Piyachat; Demba, Musa Ahmed; Kumam, Wiyada; 234808
The present paper describes the implicit fractional pantograph differential equation in the context of generalized fractional derivative and anti-periodic conditions. We formulated the Green’s function of the proposed problems. With the aid of a Green’s function, we obtain an analogous integral equation of the proposed problems and demonstrate the existence and uniqueness of solutions using the techniques of the Schaefer and Banach fixed point theorems. Besides, some special cases that show the proposed problems extend the current ones in the literature are presented. Finally, two examples were given as an application to illustrate the results obtained.
Exploring the potential of heat transfer and entropy generation of generalized dusty tetra hybrid nanofluid in a microchannel
(2024) Jarad, Fahd; Kumam, Poom; Watthayu, Wiboonsak; Jarad, Fahd; 234808
Caputo–Fabrizio time-fractional derivatives are the subject of this paper. This article generalizes the concept of dusty Tetra hybrid nanofluid moving freely via convection between infinite vertical parallel static plates. Free convection and buoyant force cause the flow and transmit the heat. In addition, there is a consistent distribution of spherical dust particles over the whole flow. It is the temperature difference between the two regions that sets off free convection. Free convection takes heat transfer into account. The dust Tetra hybrid nanofluid classical model employs non-dimensional variables to achieve a dimensionless form. We also convert the dimensionally-free model into a fractional generalized dusty Tetra hybrid nanofluid model. In this paper, we use the finite sine approach to analytically solve the governing equations of the generalized Dusty Tetra hybrid nanofluid model. In this article, we generalize the concept of a dust-filled Tetra hybrid nanofluid freely flowing between infinite vertical parallel plates. We found an analytical solution to the governing equations for the generalized dusty Tetra hybrid nanofluid by combining the Finite Sine Fourier and Laplace transforms. Understanding the mechanics of velocity and temperature profiles requires the use of numerical computation for a variety of embedded factors. In-depth statistical analysis and charting of data are features of this investigation. Using Mathcad-15, we plot the profiles of the Tetra hybrid nanofluid, dust particles, and temperatures to see the findings physically. Also determined are the skin friction and Nusselt number. The rate of heat transfer decreases with time, as seen in Table 1. Similarly, as seen in Table 2, raising the fractional parameter results in a higher skin friction. In addition, the energy profile of both velocities increases with increasing tetra hybrid nano fluid volume percent, albeit the fraction's contribution decreases with time. Since the fractional models are more accurate, they also provide more potential outcomes. When all the facts are considered, these choices may out to be the best.
Families of Travelling Waves Solutions for Fractional-Order Extended Shallow Water Wave Equations, Using an Innovative Analytical Method
(IEEE-INST Electrical Electronics Engineers INC, 2019) Baleanu, Dumitru; Shoaib; Baleanu, Dumitru; Kumam, Poom; Al-Zaidy, Jameel F.; 56389
In the present research article, an efficient analytical technique is applied for travelling waves solutions of fractional partial differential equations. The investigated problems are reduced to ordinary differential equations, by a variable transformation. The solutions of the resultant ordinary differential equations are expressed in the term of some suitable polynomials, which provide trigonometric, hyperbolic and rational function solutions with some free parameters. To confirm the reliability and novelty of the current work, the proposed method is applied for the solutions of (2+1) and (3+1)-dimensional fractional-order extended shallow water wave equations.
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.
Fractional View Analysis of Third Order Kortewege-De Vries Equations, Using a New Analytical Technique
(2020) Baleanu, Dumitru; 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.
Heat transfer analysis of unsteady MHD slip flow of ternary hybrid Casson fluid through nonlinear stretching disk embedded in a porous medium
(2024) Jarad, Fahd; Ali, Gohar; Kumam, Poom; Sitthithakerngkiet, Kanokwan; Jarad, Fahd; 234808
The original article's purpose is to assess transfer of heat exploration for unsteady magneto hydrodynamic slip flow of ternary hybrid Casson fluid via a nonlinear flexible disk placed within a perforated medium of a magnetic field in the presence. Unsteady nonlinearly stretched disk inside porous material causes flow to occur. In the investigation, convective circumstances on wall temperature are also considered. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriate transformations, and the Keller-box technique is employed for their solution. In forced convection, the variable radiation has no direct impact on fluid velocity, but it is noticed that in the case of aiding flow, fluid velocity rises with an increase in radiation parameter, and the opposite is true in the case of opposing flow. Furthermore, it is experiential that fluid concentration and velocity goes up in creative chemical reactions, and both profiles decrease in detrimental chemical reactions. Moreover, a slightly greater unsteadiness characteristic lowers fluid, concentration, temperature and velocity. Physical parameters' effects on fluid temperature, concentration, and velocity, as well as on wall shear stress, energy, and mass transfer rates, are studied.
Laplace decomposition for solving nonlinear system of fractional order partial differential equations
(2020) Baleanu, Dumitru; Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
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 operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.
Laplace decomposition for solving nonlinear system of fractional order partial differential equations
(2020) Baleanu, Dumitru; Shah, Rasool; Kumam, Poom; Baleanu, Dumitru; Arif, Muhammad; 56389
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 operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.
Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay
(MDPI, 2019) Baleanu, Dumitru; Khan, Hassan; Kumam, Poom; Arif, Muhammad; Baleanu, Dumitru; 56389
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. Natural transform decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. Therefore, Natural transform decomposition method is considered to be one of the best analytical technique, to solve fractional-order linear and non-linear Partial deferential equations particularly fractional-order partial differential equations with proportional delay.