scholarly journals One dimensional fractional frequency Sumudu transform by inverse α−difference operator

10.26524/cm73 ◽  
2020 ◽  
Vol 4 (1) ◽  
Author(s):  
Chandrasekar B ◽  
Meganathan M ◽  
Vasuki S
Keyword(s):  
Difference Operator ◽  
Convolution Product ◽  
One Dimensional ◽  
Fractional Frequency ◽  
Sumudu Transform

In this paper, we define fractional frequency Sumudu transform by inverse α−difference operator. Here we present certain new results on Sumudu transform of polynomial factorial,trigonometric and geometric functions using shift value. Finally, we provide the relation between convolution product and fractional Sumudu transform of polynomial and exponential function.Numerical results are verified and analysed the outcomes by graphs.

scholarly journals One dimensional fractional frequency Fourier transform by inverse difference operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Dumitru Baleanu ◽  
Maysaa Alqurashi ◽  
Meganathan Murugesan ◽  
Britto Antony Xavier Gnanaprakasam
Keyword(s):  
Fourier Transform ◽  
Difference Operator ◽  
One Dimensional ◽  
Fractional Frequency

scholarly journals Approximate solution for fractional attractor one-dimensional Keller-Segel equations using homotopy perturbation sumudu transform method

2020 ◽  
Vol 9 (1) ◽  
pp. 370-381
Author(s):  
Dinkar Sharma ◽  
Gurpinder Singh Samra ◽  
Prince Singh
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Simple Technique ◽  
Nonlinear Partial Differential Equations ◽  
Transform Method ◽  
Present Scheme ◽  
One Dimensional ◽  
Homotopy Perturbation ◽  
Sumudu Transform

AbstractIn this paper, homotopy perturbation sumudu transform method (HPSTM) is proposed to solve fractional attractor one-dimensional Keller-Segel equations. The HPSTM is a combined form of homotopy perturbation method (HPM) and sumudu transform using He’s polynomials. The result shows that the HPSTM is very efficient and simple technique for solving nonlinear partial differential equations. Test examples are considered to illustrate the present scheme.

scholarly journals Application of Conformable Sumudu Decomposition Method for Solving Conformable Fractional Coupled Burger’s Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Analytical Method ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
One Dimensional ◽  
Burger's Equation ◽  
Burger’S Equation ◽  
Sumudu Transform ◽  
Linear And Nonlinear

The conformable double Sumudu decomposition method (CDSDM) is a combination of decomposition method (DM) and a conformable double Sumudu transform. It is an approximate analytical method, which can be used to solve linear and nonlinear partial differential equations. In this work, one-dimensional conformable functional Burger’s equation has been solved by applying conformable double Sumudu decomposition. Two examples are used to illustrate the method.

scholarly journals n-Dimensional Fractional Frequency Laplace Transform by the Inverse Difference Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
M. Meganathan ◽  
Thabet Abdeljawad ◽  
G. Britto Antony Xavier ◽  
Fahd Jarad
Keyword(s):  
Laplace Transform ◽  
Difference Operator ◽  
Extensive Literature ◽  
Fractional Frequency ◽  
Research Article ◽  
The Laplace Transform

With the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work on n-dimensional Laplace transform. In this research article, we define n-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.

POSITIVITY OF THE INTERTWINING OPERATOR AND HARMONIC ANALYSIS ASSOCIATED WITH THE JACOBI-DUNKL OPERATOR ON ${\mathbb R}$

2003 ◽  
Vol 01 (04) ◽  
pp. 387-412 ◽  
Author(s):  
F. CHOUCHANE ◽  
M. MILI ◽  
K. TRIMÈCHE
Keyword(s):  
Integral Representation ◽  
Harmonic Analysis ◽  
Difference Operator ◽  
Convolution Product ◽  
Dunkl Transform ◽  
Dunkl Operator ◽  
Intertwining Operator ◽  
Laplace Integral ◽  
Translation Operators ◽  
Laplace Integral Representation

We consider a differential-difference operator Λα,β, [Formula: see text], [Formula: see text] on [Formula: see text]. The eigenfunction of this operator equal to 1 at zero is called the Jacobi–Dunkl kernel. We give a Laplace integral representation for this function and we prove that for [Formula: see text], [Formula: see text], the kernel of this integral representation is positive. This result permits us to prove that the Jacobi–Dunkl intertwining operator and its dual are positive. Next we study the harmonic analysis associated with the operator Λα,β (Jacobi–Dunkl transform, Jacobi–Dunkl translation operators, Jacobi–Dunkl convolution product, Paley–Wiener and Plancherel theorems…).

scholarly journals Double Sumudu Transform Iterative Method for One-Dimensional Nonlinear Coupled Sine-Gordon Equation

2022 ◽  
Vol 2022 ◽  
pp. 1-15
Author(s):  
Alemayehu Tamirie Deresse
Keyword(s):  
Iterative Method ◽  
Gordon Equation ◽  
Approximate Analytical Solution ◽  
Test Problems ◽  
Sine Gordon Equation ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Sumudu Transform ◽  
The One ◽  
The Given

In this paper, the combined double Sumudu transform with iterative method is successfully implemented to obtain the approximate analytical solution of the one-dimensional coupled nonlinear sine-Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions which cannot be solved by applying double Sumudu transform only. The solution of the nonlinear part of this equation was solved by a successive iterative method, the proposed technique has the advantage of producing an exact solution, and it is easily applied to the given problems analytically. Two test problems from mathematical physics were taken to show the liability, accuracy, convergence, and efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other types of systems of NLPDEs.

scholarly journals A new eigenvalue problem for the difference operator with nonlocal conditions

2019 ◽  
Vol 24 (3) ◽  
pp. 462-484
Author(s):  
Mifodijus Sapagovas ◽  
Regimantas Ciupaila ◽  
Kristina Jakubelienė ◽  
Stasys Rutkauskas
Keyword(s):  
Eigenvalue Problem ◽  
Difference Operator ◽  
Nonlocal Condition ◽  
Nonlocal Conditions ◽  
Theoretical Expression ◽  
Difference Problem ◽  
One Dimensional ◽  
The Difference ◽  
Degenerate Matrix ◽  
Spectrum Structure

In the paper, the spectrum structure of one-dimensional differential operator with nonlocal conditions and of the difference operator, corresponding to it, has been exhaustively investigated. It has been proved that the eigenvalue problem of difference operator is not equivalent to that of matrix eigenvalue problem Au = λu, but it is equivalent to the generalized eigenvalue problem Au = λBu with a degenerate matrix B. Also, it has been proved that there are such critical values of nonlocal condition parameters under which the spectrum of both the differential and difference operator are continuous. It has been established that the number of eigenvalues of difference problem depends on the values of these parameters. The condition has been found under which the spectrum of a difference problem is an empty set. An elementary example, illustrating theoretical expression, is presented.

scholarly journals On a class of analytic functions associated to a complex domain concerning q-differential-difference operator

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Rabha W. Ibrahim ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Existence Of Solutions ◽  
Difference Operator ◽  
Open Unit ◽  
Convolution Product ◽  
Open Unit Disk ◽  
Current Investigation ◽  
Quantum Calculus ◽  
New Class

AbstractIn our current investigation, we apply the idea of quantum calculus and the convolution product to amend a generalized Salagean q-differential operator. By considering the new operator and the typical version of the Janowski function, we designate definite new classes of analytic functions in the open unit disk. Significant properties of these modules are considered, and recurrent sharp consequences and geometric illustrations are realized. Applications are considered to find the existence of solutions of a new class of q-Briot–Bouquet differential equations.

scholarly journals Certain results on q-starlike and q-convex error functions

2018 ◽  
Vol 68 (2) ◽  
pp. 361-368 ◽  
Author(s):  
C. Ramachandran ◽  
L. Vanitha ◽  
Stanisłava Kanas
Keyword(s):  
Future Study ◽  
Difference Operator ◽  
Function Theory ◽  
Error Function ◽  
Complex Function ◽  
Mathematical Physics ◽  
Natural Sciences ◽  
Convolution Product ◽  
Complex Function Theory ◽  
The Past

Abstract The error function occurs widely in multiple areas of mathematics, mathematical physics and natural sciences. There has been no work in this area for the past four decades. In this article, we estimate the coefficient bounds with q-difference operator for certain classes of the spirallike starlike and convex error function associated with convolution product using subordination as well as quasi-subordination. Though this concept is an untrodden path in the field of complex function theory, it will prove to be an encouraging future study for researchers on error function.

ANALYTIC INVESTIGATIONS OF THE WALSH FUNCTIONS COMBINED WITH THE SUMUDU TRANSFORM AND APPLICATIONS TO THE TRANSPORT EQUATION

2011 ◽  
Vol 04 (02) ◽  
pp. 199-215
Author(s):  
Kadem Abdelouahab
Keyword(s):  
Transport Equation ◽  
Three Dimensional ◽  
Isotropic Scattering ◽  
Spectral Approximation ◽  
Infinite Domain ◽  
One Dimensional ◽  
Independent Variables ◽  
Sumudu Transform ◽  
Dimensional Equation ◽  
Transport Problems

We develop spectral approximation for solving the three-dimensional transport equation with isotropic scattering in a bounded domain. The method can be extended easily to general linear transport problem in a unbounded domain or semi infinite domain. The technique used involves the reduction of the three-dimensional equation to a system of one-dimensional equations. The idea of using the spectral method for searching solutions to the multi-dimensional transport problems, leads us to a solution for all values of the independent variables.

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