2014
2
3
3
82
Inverse SturmLiouville problems with transmission and spectral parameter boundary conditions
2
2
This paper deals with the boundary value problem involving the differential equation ell y:=y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d0), y'(d+0)=ay'(d0)+b y(d0). In this problem q(x), d, a , b are real, qin L^2(0,pi), din(0,pi) and lambda is a parameter independent of x. By defining a new Hilbert space and using spectral data of a kind, it is developed the Hochestadt's result based on transformation operator for inverse SturmLiouville problem with parameter dependent boundary and discontinuous conditions. Furthermore, it is established a formula for q(x)  tilde{q}(x) in the finite interval, where tilde{q}(x) is an analogous function with q(x).
1

123
139


Mohammad
Shahriari
University of Maragheh
University of Maragheh
I. R. Iran
shahriari@tabrizu.ac.ir
Inverse SturmLiouville problem
Jump conditions
Green's function
Eigenparameter dependent condition
Transformation operator
An analytic study on the EulerLagrange equation arising in calculus of variations
2
2
The EulerLagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the EulerLagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. Several illustrative examples are given to demonstrate the effectiveness of the present method.
1

140
152


Abbas
Saadatmandi
University of Kashan, Kashan, Iran
University of Kashan, Kashan, Iran
I. R. Iran
a.saadatmandi@gmail.com


Tahereh
AbdolahiNiasar
University of Kashan, Kashan, Iran
University of Kashan, Kashan, Iran
I. R. Iran
abdolahi.tahereh@yahoo.com
Differential transformation method
Calculus of variation
EulerLagrange equation
Variational problems
A new fractional subequation method for solving the spacetime fractional differential equations in mathematical physics
2
2
In this paper, a new fractional subequation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified RiemannLiouville derivative. With the aid of symbolic computation, we choose the spacetime fractional ZakharovKuznetsovBenjaminBonaMahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity and advantages of the novel method. As a result, some new exact solutions including solitary wave solutions and periodic wave solutions are successfully obtained. The proposed approach can also be applied to other nonlinear FPDEs arising in mathematical physics.
1

153
170


Mehmet
Ekici
Department of Mathematics, Faculty of Science and Arts, Bozok University, Yozgat, Turkey
Department of Mathematics, Faculty of Science
Turkey
mehmet.ekici@bozok.edu.tr


Abdullah
Sonmezoglu
Department of Mathematics, Faculty of Science and Arts, Bozok University, 66100 Yozgat, Turkey
Department of Mathematics, Faculty of Science
Turkey
abdullah.sonmezoglu@bozok.edu.tr


Elsayed M. E.
Zayed
Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt
Mathematics Department, Faculty of Science,
Egypt
e.m.e.zayed@hotmail.com
Fractional subequation method
fractional partial differential equations
exact solutions
modified RiemannLiouville derivative
New Solutions for Singular LaneEmden Equations Arising in Astrophysics Based on Shifted Ultraspherical Operational Matrices of Derivatives
2
2
In this paper, the ultraspherical operational matrices of derivatives are constructed. Based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear LaneEmden type singular initial value problems. The basic idea behind the suggested algorithms is basically built on transforming the equations with their initial conditions into systems of linear or nonlinear algebraic equations which can be solved by using suitable numerical solvers. The Legendre and first and second kind Chebyshev operational matrices of derivatives can be deduced as special cases of the constructed operational matrices. For the sake of testing the validity and applicability of the suggested numerical algorithms, three illustrative examples are presented.
1

171
185


Waleed
Abd Elhameed
Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
Department of Mathematics, Faculty of Science,
Egypt
walee_9@yahoo.com


Youssri
Youssri
Department of Mathematics, Faculty of Science, Cairo University, GizaEgypt
Department of Mathematics, Faculty of Science,
Egypt
youssri@sci.cu.edu.eg


Eid
Doha
Department of Mathematics, Faculty of Science, Cairo University, GizaEgypt
Department of Mathematics, Faculty of Science,
Egypt
eiddoha@sci.cu.edu.eg
Ultraspherical polynomials
operational matrix of derivatives
LaneEmden equations
isothermal gas spheres equation
Numerical inversion of Laplace transform via wavelet in ordinary differential equations
2
2
This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of listing table to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task.
1

186
194


CHUNHUI
HSIAO
No.101, Sec. 2, Jhongcheng Rd., Shihlin District, Taipei City 111, Taiwan, R.O.C.
No.101, Sec. 2, Jhongcheng Rd., Shihlin District,
Taiwan
haar.wavelet@msa.hinet.net
Haar wavelet
Inverse Laplace transform
Operational matrix of integration
Haar product matrix
Numerical solution for boundary value problem of fractional order with approximate Integral and derivative
2
2
Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three numerical examples are presented to describe the fractional usefulness of the suggested method.
1

195
204


Abdol Ali
Neamaty
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, University of
I. R. Iran
aneamaty@yahoo.com


Bahram
Agheli
Department of Mathematics, University of Mazandaran, Babolsar, Iran
Department of Mathematics, University of
I. R. Iran
b.agheli@yahoo.com


Mohammad
Adabitabar
Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran
Department of Mathematics, Qaemshahr Branch,
I. R. Iran
mohamadsadega@yahoo.com
Boundary value problems of fractional order
RiemannLiouville fractional derivative
Caputo fractional derivative
central difference