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1

Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations

E.H. Doha, A.H. Bhrawy, S.S. Ezz-Eldien

Journal:

Applied Mathematical Modelling

Year:

2011

Language:

english

File:

PDF, 313 KB

english, 2011

2

A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

E.H. Doha, A.H. Bhrawy, S.S. Ezz-Eldien

Journal:

Computers & Mathematics with Applications

Year:

2011

Language:

english

File:

PDF, 249 KB

english, 2011

3

Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method

A.H. Bhrawy, M.A. Abdelkawy, Anjan Biswas

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2013

Language:

english

File:

PDF, 640 KB

english, 2013

4

Wavelet based spectral analysis of optical solitons

Hilal, E.M., Alshaery, A.A., Bhrawy, A.H., Bhosale, Bharat, Biswas, Anjan

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2014

Language:

english

File:

PDF, 352 KB

english, 2014

5

Optical solitons in birefringent fibers with spatio-temporal dispersion

Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Savescu, Michelle, Milovic, Daniela, Khan, Kaisar R., Mahmood, Mohammad F., Jovanoski, Zlatko, Biswas, Anjan

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2014

Language:

english

File:

PDF, 489 KB

english, 2014

6

A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems

Ezz-Eldien, S., Doha, E., Baleanu, D., Bhrawy, A.

Journal:

Journal of Vibration and Control

Year:

2015

Language:

english

File:

PDF, 701 KB

english, 2015

7

Shifted fractional-order Jacobi orthogonal functions: Application to a system of fractional differential equations

Bhrawy, A.H., Zaky, M.A.

Journal:

Applied Mathematical Modelling

Year:

2015

Language:

english

File:

PDF, 401 KB

english, 2015

8

A new Legendre operational technique for delay fractional optimal control problems

Bhrawy, A. H., Ezz-Eldien, S. S.

Journal:

Year:

2016

Language:

english

File:

PDF, 688 KB

english, 2016

9

The operational matrix of Caputo fractional derivatives of modified generalized Laguerre polynomials and its applications

Bhrawy, Ali H, Alghamdi, Mohammed A

Journal:

Advances in Difference Equations

Year:

2013

Language:

english

File:

PDF, 564 KB

english, 2013

10

Solving fractional optimal control problems within a Chebyshev–Legendre operational technique

Bhrawy, A. H., Ezz-Eldien, S. S., Doha, E. H., Abdelkawy, M. A., Baleanu, D.

Journal:

International Journal of Control

Year:

2017

Language:

english

File:

PDF, 574 KB

english, 2017

11

A Jacobi–Gauss collocation method for solving nonlinear Lane–Emden type equations

A.H. Bhrawy, A.S. Alofi

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2012

Language:

english

File:

PDF, 284 KB

english, 2012

12

Jacobi Pseudo-Spectral Method JPSM and BPES for Solving Differential Equations

A. H. Bhrawy, A. Rezaei, K. Boubaker

Journal:

Differential Equations and Dynamical Systems

Year:

2012

Language:

english

File:

PDF, 371 KB

english, 2012

13

A new Jacobi operational matrix: An application for solving fractional differential equations

E.H. Doha, A.H. Bhrawy, S.S. Ezz-Eldien

Journal:

Applied Mathematical Modelling

Year:

2012

Language:

english

File:

PDF, 296 KB

english, 2012

14

An efficient direct solver for multidimensional elliptic Robin boundary value problems using a Legendre spectral-Galerkin method

E.H. Doha, A.H. Bhrawy

Journal:

Computers & Mathematics with Applications

Year:

2012

Language:

english

File:

PDF, 328 KB

english, 2012

15

A Jacobi elliptic function method for nonlinear arrays of vortices

A. H. Bhrawy, M. M. Tharwat, A. Yildirim, M. A. Abdelkawy

Journal:

Indian Journal of Physics

Year:

2012

Language:

english

File:

PDF, 838 KB

english, 2012

16

A shifted Jacobi-Gauss-Lobatto collocation method for solving nonlinear fractional Langevin equation involving two fractional orders in different intervals

Ali H Bhrawy, Mohammed A Alghamdi

Journal:

Boundary Value Problems

Year:

2012

Language:

english

File:

PDF, 636 KB

english, 2012

17

A new formula for fractional integrals of Chebyshev polynomials: Application for solving multi-term fractional differential equations

Bhrawy, A.H., Tharwat, M.M., Yildirim, A.

Journal:

Applied Mathematical Modelling

Year:

2013

Language:

english

File:

PDF, 199 KB

english, 2013

18

On shifted Jacobi spectral approximations for solving fractional differential equations

Doha, E.H., Bhrawy, A.H., Baleanu, D., Ezz-Eldien, S.S.

Journal:

Applied Mathematics and Computation

Year:

2013

Language:

english

File:

PDF, 388 KB

english, 2013

19

Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method

Doha, Eid H., Bhrawy, Ali H., Ezz-Eldien, Samer S.

Journal:

Central European Journal of Physics

Year:

2013

Language:

english

File:

PDF, 435 KB

english, 2013

20

Optical solitons in (1+1) and (2+1) dimensions

Bhrawy, A.H., Abdelkawy, M.A., Biswas, Anjan

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2014

Language:

english

File:

PDF, 709 KB

english, 2014

21

A Spectral Legendre–Gauss–Lobatto Collocation Method for a Space-Fractional Advection Diffusion Equations with Variable Coefficients

Bhrawy, A.H., Baleanu, D.

Journal:

Reports on Mathematical Physics

Year:

2013

Language:

english

File:

PDF, 1.03 MB

english, 2013

22

Thirring optical solitons with Kerr law nonlinearity

Biswas, Anjan, Bhrawy, A.H., Alshaery, A.A., Hilal, E.M.

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2014

Language:

english

File:

PDF, 322 KB

english, 2014

23

Optical Solitons in Magneto-optic Waveguides with Spatio-temporal Dispersion

Savescu, Michelle, Bhrawy, A. H., Hilal, E. M., Alshaery, A. A., Biswas, Anjan

Journal:

Year:

2014

Language:

english

File:

PDF, 132 KB

english, 2014

24

Optical soliton perturbation with spatio-temporal dispersion in parabolic and dual-power law media by semi-inverse variational principle

Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Khan, Kaisar R., Mahmood, Mohammad F., Biswas, Anjan

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2014

Language:

english

File:

PDF, 409 KB

english, 2014

25

Bright and dark solitons in a cascaded system

Bhrawy, A.H., Alshaery, A.A., Hilal, E.M., Jovanoski, Zlatko, Biswas, Anjan

Journal:

Optik - International Journal for Light and Electron Optics

Year:

2014

Language:

english

File:

PDF, 299 KB

english, 2014

26

A numerical technique based on the shifted Legendre polynomials for solving the time-fractional coupled KdV equations

Bhrawy, A. H., Doha, E. H., Ezz-Eldien, S. S., Abdelkawy, M. A.

Journal:

Year:

2016

Language:

english

File:

PDF, 486 KB

english, 2016

27

A space-time Legendre spectral tau method for the two-sided space-time Caputo fractional diffusion-wave equation

Bhrawy, A. H., Zaky, M. A., Van Gorder, R. A.

Journal:

Numerical Algorithms

Year:

2016

Language:

english

File:

PDF, 595 KB

english, 2016

28

Two Efficient Generalized Laguerre Spectral Algorithms for Fractional Initial Value Problems

Baleanu, D., Bhrawy, A. H., Taha, T. M.

Journal:

Abstract and Applied Analysis

Year:

2013

Language:

english

File:

PDF, 288 KB

english, 2013

29

A New Numerical Algorithm for Solving a Class of Fractional Advection-Dispersion Equation with Variable Coefficients Using Jacobi Polynomials

Journal:

Abstract and Applied Analysis

Year:

2013

Language:

english

File:

PDF, 816 KB

english, 2013

30

A New Legendre Spectral Galerkin and Pseudo-Spectral Approximations for Fractional Initial Value Problems

Bhrawy, A. H., Alghamdi, M. A.

Journal:

Abstract and Applied Analysis

Year:

2013

Language:

english

File:

PDF, 548 KB

english, 2013

31

A New Legendre Collocation Method for Solving a Two-Dimensional Fractional Diffusion Equation

Journal:

Abstract and Applied Analysis

Year:

2014

Language:

english

File:

PDF, 1.07 MB

english, 2014

32

A Jacobi spectral collocation method for solving multi-dimensional nonlinear fractional sub-diffusion equations

Journal:

Numerical Algorithms

Year:

2016

Language:

english

File:

PDF, 1.46 MB

english, 2016

33

Numerical algorithm for the variable-order Caputo fractional functional differential equation

Bhrawy, A. H., Zaky, M. A.

Journal:

Nonlinear Dynamics

Year:

2016

Language:

english

File:

PDF, 520 KB

english, 2016

34

On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations

Doha, E. H., Bhrawy, A. H., Saker, M. A.

Journal:

Boundary Value Problems

Year:

2011

Language:

english

File:

PDF, 279 KB

english, 2011

35

New spectral collocation algorithms for one- and two-dimensional Schrödinger equations with a Kerr law nonlinearity

Bhrawy, Ali H, Mallawi, Fouad, Abdelkawy, Mohamed A

Journal:

Advances in Difference Equations

Year:

2016

Language:

english

File:

PDF, 1.85 MB

english, 2016

36

An improved collocation method for multi-dimensional space–time variable-order fractional Schrödinger equations

Bhrawy, A.H., Zaky, M.A.

Journal:

Applied Numerical Mathematics

Year:

2016

Language:

english

File:

PDF, 463 KB

english, 2016

37

Two shifted Jacobi-Gauss collocation schemes for solving two-dimensional variable-order fractional Rayleigh-Stokes problem

Bhrawy, Ali H, Zaky, Mahmoud A, Alzaidy, Jameel F

Journal:

Advances in Difference Equations

Year:

2016

Language:

english

File:

PDF, 2.50 MB

english, 2016

38

Direct numerical method for isoperimetric fractional variational problems based on operational matrix

Ezz–Eldien, Samer S, Bhrawy, Ali H, El–Kalaawy, Ahmed A

Journal:

Journal of Vibration and Control

Year:

2017

Language:

english

File:

PDF, 579 KB

english, 2017

39

A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations

Eid H. Doha, Ali H. Bhrawy

Journal:

Numerical Methods for Partial Differential Equations

Year:

2009

Language:

english

File:

PDF, 305 KB

english, 2009

40

Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials

E.H. Doha, A.H. Bhrawy

Journal:

Applied Numerical Mathematics

Year:

2008

Language:

english

File:

PDF, 218 KB

english, 2008

41

Jacobi spectral Galerkin method for the integrated forms of second-order differential equations

A.H. Bhrawy, S.I. El-Soubhy

Journal:

Applied Mathematics and Computation

Year:

2010

Language:

english

File:

PDF, 269 KB

english, 2010

42

Integrals of Bernstein polynomials: An application for the solution of high even-order differential equations

E.H. Doha, A.H. Bhrawy, M.A. Saker

Journal:

Applied Mathematics Letters

Year:

2011

Language:

english

File:

PDF, 225 KB

english, 2011

43

A Jacobi–Jacobi dual-Petrov–Galerkin method for third- and fifth-order differential equations

E.H. Doha, A.H. Bhrawy, R.M. Hafez

Journal:

Mathematical and Computer Modelling

Year:

2011

Language:

english

File:

PDF, 282 KB

english, 2011

44

Efficient spectral-Galerkin algorithms for direct solution for second-order differential equations using Jacobi polynomials

E. H. Doha, A. H. Bhrawy

Journal:

Numerical Algorithms

Year:

2006

Language:

english

File:

PDF, 356 KB

english, 2006

45

Jacobi spectral Galerkin method for elliptic Neumann problems

E. H. Doha, A. H. Bhrawy, W. M. Abd-Elhameed

Journal:

Numerical Algorithms

Year:

2009

Language:

english

File:

PDF, 444 KB

english, 2009

46

A quadrature tau method for fractional differential equations with variable coefficients

A.H. Bhrawy, A.S. Alofi, S.S. Ezz-Eldien

Journal:

Applied Mathematics Letters

Year:

2011

Language:

english

File:

PDF, 222 KB

english, 2011

47

Efficient spectral ultraspherical-Galerkin algorithms for the direct solution of 2nth-order linear differential equations

E.H. Doha, W.M. Abd-Elhameed, A.H. Bhrawy

Journal:

Applied Mathematical Modelling

Year:

2009

Language:

english

File:

PDF, 270 KB

english, 2009

48

Polytropic star structure analysis under Bonnor–Ebert gas sphere astrophysical configuration thorough investigating analytical solutions to the related Lane–Emden equation

K. Boubaker, A.H. Bhrawy

Journal:

Advances in Space Research

Year:

2012

Language:

english

File:

PDF, 534 KB

english, 2012

49

On shifted Jacobi spectral method for high-order multi-point boundary value problems

E.H. Doha, A.H. Bhrawy, R.M. Hafez

Journal:

Communications in Nonlinear Science and Numerical Simulation

Year:

2012

Language:

english

File:

PDF, 227 KB

english, 2012

50

A shifted Legendre spectral method for fractional-order multi-point boundary value problems

Ali H Bhrawy, Mohammed M Al-Shomrani

Journal:

Advances in Difference Equations

Year:

2012

Language:

english

File:

PDF, 254 KB

english, 2012