The fractional q-differential transformation and its application

El-Shahed, Moustafa; Gaber, M.; Alyami, Maryam Ahmed

doi:10.1016/j.cnsns.2012.06.016

Cited by 9 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the solution of fractional integro-differential equations (FIDEs) various numerical method have been used over the years, some of these may be found in the references [9,25,26,32,33]. Brunner and co-authors have developed very efficient collocation methods for the solution of Volterra integral equations, some of these can be found in the references [2,3,7], and some other accurate numerical methods are referred in [8,27,31,42]. Several mathematical models and simulations of real world problems usually expressed in terms of functional equations.…”

Section: (13) C 2020 Miskolc University Pressmentioning

confidence: 99%

On the local transformed based method for partial integro-differential equations of fractional order

Uddin¹,

Taufiq²

2020

MMN

View full text Add to dashboard Cite

In the present work, a localized Laplace transform based numerical scheme is constructed for fractional partial integro-differential equations with weakly singular kernels. By application of the Laplace transform the time variable is eliminated and the spatial derivatives are approximated by RBF which transformed the problem into a linear system of equations. The resultant system lead to differentiation matrices which are sparse contrary to large global collocation matrices. The inverse Laplace transform is then computed numerically using contour integration to recover the solution. The efficiency and accuracy of the method is demonstrated by several numerical experiments. The results obtained by the present method are compared with analytical solutions and other numerical methods.

show abstract

Section: (13) C 2020 Miskolc University Pressmentioning

confidence: 99%

On the local transformed based method for partial integro-differential equations of fractional order

Uddin¹,

Taufiq²

2020

MMN

View full text Add to dashboard Cite

show abstract

“…The q-analog of TDDTM (TDq-DTM) was investigated in [13,17], and a non-linear q-Schrödinger equation was solved in [18] using this method. The fractional q-DTM to solve fractional q-DEs was constructed in [9,14]. The q-analog of RDTM (Rq-DTM) was presented in [22,32].…”

Section: Introductionmentioning

confidence: 99%

On q,ω -differential transform method

Hıra¹

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

In this study, the differential transform method (DTM) associated with the Hahn difference operator ( D q , ω ) has been examined. The definitions and theorems of the one and two-dimensional q , ω -DTM are introduced. Then, the presented q , ω -DTMs are applied to obtain the analytical or approximation solution of linear or non-linear q , ω -initial value problems consisting of the q , ω -ordinary or q , ω -partial differential equation.

show abstract

“…It has a variety of uses in mathematics, engineering and science, including basic hypergeometric functions [35], orthogonal polynomials [25], combinatorics [19], and quantum theory [21]. In recent years, several scholars have attempted to solve many types of q-DEs by using semianalytic methods, including; the q-differential transformation method (q-DTM) [12], [13], variational iteration method [39], successive approximation method, and homotopy analysis method [36].…”

Section: Introductionmentioning

confidence: 99%

Solving Riccati Type q−Difference Equations via Difference Transform Method

Khudair¹,

Abdulmajeed²

2021

Al-Qadisiyah Journal of Pure Science

View full text Add to dashboard Cite

In this paper, we deal on the time scale that its delta derivative of graininess function is a nonzero positive constant. Based on the Taylor formula for this time scale, we investigate the difference transform method (DTM). This method has been applied successfully to solve Riccati type difference equations in quantum calculus. To demonstrate the ability and efficacy of this method, some examples have been provided.

show abstract

The fractional q-differential transformation and its application

Cited by 9 publications

References 16 publications

On the local transformed based method for partial integro-differential equations of fractional order

On the local transformed based method for partial integro-differential equations of fractional order

On q,ω -differential transform method

Solving Riccati Type q−Difference Equations via Difference Transform Method

Contact Info

Product

Resources

About