On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

Talib, Imran; Belgacem, Fethi Bin Muhammad; Asif, Naseer Ahmad; Khalil, Hammad

doi:10.1063/1.4972616

Cited by 6 publications

(4 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 3.1: Let N 2 (x, y) be the shifted Legendre function vector of dimensions N 2 × 1, defined in (13), then…”

Section: Resultsmentioning

confidence: 99%

“…Let (x, y) be the shifted Legendre function vector in two variables defined in (13), and also assume that η > 0, then…”

Section: Lemma 23mentioning

confidence: 99%

“…In recent years, several methods have been developed to solve FDEs, FOPDEs, and dynamic systems formulated using mathematical tools from FC. The names of few of them are Galerkin method [8], collocation method [9], Adomian's decomposition method [10,11], and operational matrices approach [12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New operational matrices of orthogonal Legendre polynomials and their operational

Talib

Tunç

Noor

2019

Journal of Taibah University for Science

Self Cite

View full text Add to dashboard Cite

Many conventional physical and engineering phenomena have been identified to be well expressed by making use of the fractional order partial differential equations (FOPDEs). For that reason, a proficient and stable numerical method is needed to find the approximate solution of FOPDEs. This article is designed to develop the numerical scheme able to find the approximate solution of generalized fractional order coupled systems (FOCSs) with mixed partial derivative terms of fractional order. Our main objective in this article is the development of a new operational matrix for fractional mixed partial derivatives based on the orthogonal shifted Legendre polynomials (SLPs). The fractional derivatives are considered herein in the sense of Caputo. The proposed method has the advantage to reduce the considered problems to a system of algebraic equations which are simple in handling by any computational software. Being easily solvable, the associated algebraic system leads to finding the solution of the problem. Some examples are included to demonstrate the accuracy and validity of the proposed method. ARTICLE HISTORY

show abstract

“…Theorem 3.1: Let N 2 (x, y) be the shifted Legendre function vector of dimensions N 2 × 1, defined in (13), then…”

Section: Resultsmentioning

confidence: 99%

“…Let (x, y) be the shifted Legendre function vector in two variables defined in (13), and also assume that η > 0, then…”

Section: Lemma 23mentioning

confidence: 99%

See 1 more Smart Citation

New operational matrices of orthogonal Legendre polynomials and their operational

Talib

Tunç

Noor

2019

Journal of Taibah University for Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…For finding the solution of differential and integral equations, operational matrices have been developed of the polynomials such as Walsh operational matrices, block pulse operational matrices, generalized block pulse operational matrices, Haar wavelet, Legendre wavelet, Bernoulli wavlet operational matrix, Jacobi operational matrix, and Chebyshev wavelet operational matrices . These references show the good dimensions of adopting operational matrices.…”

Section: Introductionmentioning

confidence: 99%

Numerical inversion of Laplace transform based on Bernstein operational matrix

Rani

Mishra

Cattani

2018

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper provides a technique to investigate the inverse Laplace transform by using orthonormal Bernstein operational matrix of integration. The proposed method is based on replacing the unknown function through a truncated series of Bernstein basis polynomials and the coefficients of the expansion are obtained using the operational matrix of integration. This is an alternative procedure to find the inversion of Laplace transform with few terms of Bernstein polynomials.Numerical tests on various functions have been performed to check the applicability and efficiency of the technique. The root mean square error between exact and numerical results is computed, which shows that the method produces the satisfactory results. A rough upper bound for errors is also estimated. KEYWORDSLaplace transform, numerical inverse Laplace transform, operational matrices, orthonormal Bernstein polynomialswhere c is a positive real number and all the poles of F(s) lie at the left side of the line s = c. Sometimes, inverse Laplace transform becomes complicated when the analytic inverse cannot be found. Hence, to calculate the inverse Laplace transform, numerical techniques are adopted.Recently, numerous different methods have been adopted for analytically and numerically inverting the Laplace transform, which is well suited to different types of functions. Lee and Sheen 5 developed analytic continuation of Bromwich integral and determined the integral by using quadrature rule, Dubner and Abate 6 expressed the function in Fourier cosine series, further it was improved by Durbin 7 that the trapezoidal rule can be applied and the function can be expressed in trigonometric series, Iqbal 8 studied the regularization method, Cuomo et al 9 have described a numerical technique based Math Meth Appl Sci. 2018;41:9231-9243.wileyonlinelibrary.com/journal/mma

show abstract

Hyers–Ulam Stability of a Class of Nonlocal Boundary Value Problem Having Triple Solutions

Ali

Fatima

Shah

et al. 2017

Int. J. Appl. Comput. Math

View full text Add to dashboard Cite

On mixed derivatives type high dimensional multi-term fractional partial differential equations approximate solutions

Cited by 6 publications

References 24 publications

New operational matrices of orthogonal Legendre polynomials and their operational

New operational matrices of orthogonal Legendre polynomials and their operational

Numerical inversion of Laplace transform based on Bernstein operational matrix

Hyers–Ulam Stability of a Class of Nonlocal Boundary Value Problem Having Triple Solutions

Contact Info

Product

Resources

About