In this article,several theorems of fractional conformable derivatives and triple Sumudu transform are given and proved.Based on these theorems,a new conformable triple Sumudu decomposition method(CTSDM)is intrduced f...In this article,several theorems of fractional conformable derivatives and triple Sumudu transform are given and proved.Based on these theorems,a new conformable triple Sumudu decomposition method(CTSDM)is intrduced for the solution of singular two-dimensional conformable functional Burger's equation.This method is a combination of the decomposition method(DM)and Conformable triple Sumudu transform.The exact and approximation solutions obtained by using the suggested method in the sense of conformable.Particular examples are given to clarify the possible application of the achieved results and the exact and approximate solution are sketched by using Matlab software.展开更多
In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method.The fractiona...In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method.The fractional derivatives are described in the Caputo sense.The applications related to Sumudu transform method and Hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations.展开更多
This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. T...This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.展开更多
Unlike the traditional Laplace transform, the Sumudu transform of a function, when approximated as a power series, may be readily inverted using factorial-based coefficient diminution. This technique offers straightfo...Unlike the traditional Laplace transform, the Sumudu transform of a function, when approximated as a power series, may be readily inverted using factorial-based coefficient diminution. This technique offers straightforward computational advantages for approximate range-limited numerical solutions of certain ordinary, mixed, and partial linear differential and integro-differential equations. Furthermore, discrete convolution (the Cauchy product), may also be utilized to assist in this approximate inversion method of the Sumudu transform. Illustrative examples are provided which elucidate both the applicability and limitations of this method.展开更多
In this paper, we present a comparative study between the modified Sumudu decomposition method (MSDM) and homotopy perturbation method (HPM). The study outlines the important features of the two methods. The analysis ...In this paper, we present a comparative study between the modified Sumudu decomposition method (MSDM) and homotopy perturbation method (HPM). The study outlines the important features of the two methods. The analysis will be explained by discussing the nonhomogeneous Kortewege-de Vries (KdV) problems.展开更多
The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, a...The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.展开更多
This article presents some important results of conformable fractional partial derivatives.The conformable triple Laplace and Sumudu transform are coupled with the Adomian decomposition method where a new method is pr...This article presents some important results of conformable fractional partial derivatives.The conformable triple Laplace and Sumudu transform are coupled with the Adomian decomposition method where a new method is proposed to solve nonlinear partial differential equations in 3-space.Moreover,mathematical experiments are provided to verify the performance of the proposed method.A fundamental question that is treated in this work:is whether using the Laplace and Sumudu transforms yield the same results?This question is amply answered in the realm of the proposed applications.展开更多
In this paper, we define Sumudu transform with convergence conditions in bicomplex space. Also, we derive some of its basic properties and its inverse. Applications of bicomplex Sumudu transform are illustrated to fin...In this paper, we define Sumudu transform with convergence conditions in bicomplex space. Also, we derive some of its basic properties and its inverse. Applications of bicomplex Sumudu transform are illustrated to find the solution of differential equation of bicomplex-valued functions and find the solution for Cartesian transverse electric magnetic （TEM） waves in homogeneous space.展开更多
In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integr...In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.展开更多
We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modi...We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modified Homotopy Perturbation Method (MHPM), The Homotopy Perturbation and Sumudu Transform Method. The results achieved using the both methods are the same. However, we calculate the approached theoretical solution of the Black-Scholes model in the form of a convergent power series with a regularly calculated element. Finally, we propose a descriptive example to demonstrate the efficiency and the simplicity of the methods.展开更多
In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation ...In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation of the original function. Various analytic consequent results are given. The simplicity and efficacy of the method are illustrated through many examples with shown Maple graphs, and transform tables are provided. Finally, a new infinite series representation related to Laplace transforms of trigonometric functions is proposed.展开更多
This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation play...This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.展开更多
In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)...In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.展开更多
In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long w...In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave(RLW)equations.The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans.The derived results are very significant and imperative for explaining various physical phenomenons.The suggested method basically demonstrates how two efficient techniques,the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations.The nonlinear expressions can be simply managed by application of He’s polynomials.The result shows that the HPSTM is very powerful,efficient,and simple and it eliminates the round-off errors.It has been observed that the proposed technique can be widely employed to examine other real world problems.展开更多
基金The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding this Research group No(RG-1440-030).
文摘In this article,several theorems of fractional conformable derivatives and triple Sumudu transform are given and proved.Based on these theorems,a new conformable triple Sumudu decomposition method(CTSDM)is intrduced for the solution of singular two-dimensional conformable functional Burger's equation.This method is a combination of the decomposition method(DM)and Conformable triple Sumudu transform.The exact and approximation solutions obtained by using the suggested method in the sense of conformable.Particular examples are given to clarify the possible application of the achieved results and the exact and approximate solution are sketched by using Matlab software.
文摘In this paper we are looking forward to finding the approximate analytical solutions for fractional integro-differential equations by using Sumudu transform method and Hermite spectral collocation method.The fractional derivatives are described in the Caputo sense.The applications related to Sumudu transform method and Hermite spectral collocation method have been developed for differential equations to the extent of access to approximate analytical solutions of fractional integro-differential equations.
文摘This paper extends the homotopy perturbation Sumudu transform method (HPSTM) to solve linear and nonlinear fractional Klein-Gordon equations. To illustrate the reliability of the method, some examples are presented. The convergence of the HPSTM solutions to the exact solutions is shown. As a novel application of homotopy perturbation sumudu transform method, the presented work showed some essential difference with existing similar application four classical examples also highlighted the significance of this work.
文摘Unlike the traditional Laplace transform, the Sumudu transform of a function, when approximated as a power series, may be readily inverted using factorial-based coefficient diminution. This technique offers straightforward computational advantages for approximate range-limited numerical solutions of certain ordinary, mixed, and partial linear differential and integro-differential equations. Furthermore, discrete convolution (the Cauchy product), may also be utilized to assist in this approximate inversion method of the Sumudu transform. Illustrative examples are provided which elucidate both the applicability and limitations of this method.
文摘In this paper, we present a comparative study between the modified Sumudu decomposition method (MSDM) and homotopy perturbation method (HPM). The study outlines the important features of the two methods. The analysis will be explained by discussing the nonhomogeneous Kortewege-de Vries (KdV) problems.
基金Project supported by the DST-FIST Program for Higher Education Institutions of India(No. SR/FST/MS-I/2018/23(C))。
文摘The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.
文摘This article presents some important results of conformable fractional partial derivatives.The conformable triple Laplace and Sumudu transform are coupled with the Adomian decomposition method where a new method is proposed to solve nonlinear partial differential equations in 3-space.Moreover,mathematical experiments are provided to verify the performance of the proposed method.A fundamental question that is treated in this work:is whether using the Laplace and Sumudu transforms yield the same results?This question is amply answered in the realm of the proposed applications.
文摘In this paper, we define Sumudu transform with convergence conditions in bicomplex space. Also, we derive some of its basic properties and its inverse. Applications of bicomplex Sumudu transform are illustrated to find the solution of differential equation of bicomplex-valued functions and find the solution for Cartesian transverse electric magnetic （TEM） waves in homogeneous space.
文摘In the present paper, the authors introduce a new integral transform which yields a number of potentially useful （known or new） integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude （for example） existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given.
文摘We introduce two algorithms in order to find the exact solution of the nonlinear Time-fractional Partial differential equation, in this research work. Those algorithms are proposed in the following structure: The Modified Homotopy Perturbation Method (MHPM), The Homotopy Perturbation and Sumudu Transform Method. The results achieved using the both methods are the same. However, we calculate the approached theoretical solution of the Black-Scholes model in the form of a convergent power series with a regularly calculated element. Finally, we propose a descriptive example to demonstrate the efficiency and the simplicity of the methods.
文摘In this paper, the Laplace transform definition is implemented without resorting to Adomian decomposition nor Homotopy perturbation methods. We show that the said transform can be simply calculated by differentiation of the original function. Various analytic consequent results are given. The simplicity and efficacy of the method are illustrated through many examples with shown Maple graphs, and transform tables are provided. Finally, a new infinite series representation related to Laplace transforms of trigonometric functions is proposed.
文摘This article is devoted to a newly introduced numerical method for time-fractional dispersive partial differential equation in a multidimensional space.The time-fractional dispersive partial differential equation plays a great role in solving the problems arising in ocean science and engineering.The numerical technique comprises of Sumudu transform,homotopy perturbation scheme and He’s polynomial,namely homotopy perturbation Sumudu transform method(HPSTM)is efficiently used to examine time-fractional dispersive partial differential equation of third order in multi-dimensional space.The approximate analytic solution of the time-fractional dispersive partial differential equation of third-order in multi-dimensional space obtained by HPSTM is compared with exact solution as well as the solution obtained by using Adomain decomposition method.The results derived with the aid of two techniques are in a good agreement and consequently these techniques may be considered as an alternative and efficient approach for solving fractional partial differential equations.Several test problems are experimented to confirm the accuracy and efficiency of the proposed methods.
文摘In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.
文摘In this work,we apply an efficient analytical algorithm namely homotopy perturbation Sumudu transform method(HPSTM)to find the exact and approximate solutions of linear and nonlinear time-fractional regularized long wave(RLW)equations.The RLW equations describe the nature of ion acoustic waves in plasma and shallow water waves in oceans.The derived results are very significant and imperative for explaining various physical phenomenons.The suggested method basically demonstrates how two efficient techniques,the Sumudu transform scheme and the homotopy perturbation technique can be integrated and applied to find exact and approximate solutions of linear and nonlinear time-fractional RLW equations.The nonlinear expressions can be simply managed by application of He’s polynomials.The result shows that the HPSTM is very powerful,efficient,and simple and it eliminates the round-off errors.It has been observed that the proposed technique can be widely employed to examine other real world problems.
