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2013
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Solving Fractional Partial Differential Equation by Using Wavelet Operational Method
Solving Fractional Partial Differential Equation by Using Wavelet Operational Method
en
en
In this paper, we use a method based on the operational matrices to the solution of the fractional partial differential equations. The main approach is based on the operational matrices of the Haar wavelets to obtain the algebraic equations. The fractional derivatives are described in Caputo sense. Some examples are included to demonstrate the validity and applicability of the techniques.
230
240
A.
Neamaty
B.
Agheli
R.
Darzi
Operational matrix
Fractional partial differential equation
Haar wavelets
Numerical method.
Article.1.pdf
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]
Approximate Solutions of the Q-discrete Burgers Equation
Approximate Solutions of the Q-discrete Burgers Equation
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en
Q-difference equations are a class of non-classical models. In this study, a combined method which has the merits of the varitional iteration method and the Adomian decomposition method is proposed. Then, the method is applied to a q-Burgers equation and approximate solutions are obtained.
241
248
Yu-xiang
Zeng
Yi
Zeng
Variational iteration method
Adomian decomposition method
Q-Burgers equation
Article.2.pdf
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S. Das, R. K. Gupta, Approximate analytical solutions of time-space fractional diffusion equation by Adomian decomposition method and homotopy perturbation method, Communications in Fractional Calculus, 2 (2011), 29-35
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G. C. Wu, Adomian decomposition method for non-smooth initial value problems, Mathematical and Computer Modelling, 54 (2011), 2104-2108
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J. S. Duan, R. Rach, D. Buleanu, A. M. Wazwaz, A review of the Adomian decomposition method and its applications to fractional differential equations, Communications in Fractional Calculus, 3 (2012), 73-99
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S. Abbasbandy, A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials, Journal of Computational and Applied Mathematics, 207 (2007), 59-63
]
Conformal H-vector-change in Finsler Spaces
Conformal H-vector-change in Finsler Spaces
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en
We investigate what we call a conformal \(h\)-vector-change in Finsler spaces, namely
\[F(x,y)\rightarrow\bar{F}(x,y)=e^{\sigma(x)}F(x,y)+\beta ,\]
where, \(\sigma\) is a function of \(x\) only, and \(\beta(x,y):=b_i(x,y)y^i\), where \(b_i:=b_i(x,y)\) is an \(h\)-vector. This change generalizes various types of changes: conformal changes, generalized Randers changes, Randers change. Under this change, we obtain the relationships between some tensors associated with \((M,F)\) and the corresponding tensors associated with \((M,\bar{F})\). Next, we express the conditions for more generalized \(m\)-th root metrics \(\tilde{F}_1=\sqrt{A_1^{\frac{2}{m_1}}+B_1+C_1}\) and \(\tilde{F}_2=\sqrt{A_2^{\frac{2}{m_2}}+B_2+C_2}\), when is established conformal \(h\)-vector-change and \(m_1, m_2\) are even numbers and other case \(m_1, m_2\) even and odd numbers, respectively. Finally, we prove that under these conditions conformal \(h\)-vector-change in Finsler spaces reduces to conformal \(\beta\)-change in Finsler spaces.
249
257
A.
Taleshian
D. M.
Saghali
S. A.
Arabi
\(m\)-th root metric
more generalized \(m\)-th root metric
generalized Randers change.
Article.3.pdf
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]
Difference Equations and Sbec Optimal Codes
Difference Equations and Sbec Optimal Codes
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en
This paper studies the patterns of the solutions of an equation on bounds for one kind of optimal codes that corrects all solid bursts of length b or less and no others. Difference equations that are satisfied by the solutions (namely the parameters-the code length and information digits of such codes) are obtained.
258
265
P. K.
Das
Parity check digits
bounds
solid burst error
optimal codes
difference equation.
Article.4.pdf
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P. K. Das, Codes Detecting and Correcting Solid Burst Errors, Bulletin of Electrical Engineering and Informatics, 1(3) (2012), 225-232
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]
Introducing a Novel Bivariate Generalized Skew-symmetric Normal Distribution
Introducing a Novel Bivariate Generalized Skew-symmetric Normal Distribution
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en
We introduce a generalization of the bivariate generalized skew-symmetric normal distribution [5]. We
denote this distribution by \(SGN_ n (\lambda_1,\lambda_2 )\) . We obtain some properties of \(SGN_ n (\lambda_1,\lambda_2 )\) and derive the
moment generating function.
266
271
Behrouz
Fathi-vajargah
Parisa
Hasanalipour
Generalized-skew-normal distribution
\(SGN_ n (\lambda_1
\lambda_2 )\)
Conditional distribution.
Article.5.pdf
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R. B. Arellano-Valle, H. W. Gomez, F. A. Quintana, A new class of skew-normal distribution, Commun. Stat Theory Methods, 33(7) (2004), 1465-1480
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]
New Homotopy Perturbation Method to Solve Non-linear Problems
New Homotopy Perturbation Method to Solve Non-linear Problems
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en
In this article, we introduce a new homotopy perturbation method (NHPM) for solving non-linear
problems, such that it can be converted a non-linear differential equations to some simple linear
differential. We will solve linear differential equation by using analytic method that it is better
than the variational iteration method and to find parameter \(\alpha\), we use projection method, which
is easier and decrease computations in comparison with similar works. Also in some of the
references perturbation method are depend on small parameter but in our proposed method it is
not depend on small parameter, finally we will solve some example for illustrating validity and
applicability of the proposed method.
272
275
M.
Rabbani
Non-linear
Differential Equations
Homotopy
Perturbation
Galerkin Method.
Article.6.pdf
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A. Glayeri, M. Rabbani, New Technique in Semi-Analytic Method for Solving Non-Linear Differential Equations, Mathematical Sciences, Vol 5, No.4 (2011), 397-406
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]
Coupled Fixed Point Theorems for Symmetric \((\phi,\psi )\)-weakly Contractive Mappings in Ordered Partial Metric Spaces
Coupled Fixed Point Theorems for Symmetric \((\phi,\psi )\)-weakly Contractive Mappings in Ordered Partial Metric Spaces
en
en
We establish some coupled fixed point theorems for symmetric \((\phi,\psi)\)-weakly contractive mappings in ordered partial metric spaces. Some recent results of Berinde (Nonlinear Anal. 74 (2011), 7347-7355; Nonlinear Anal. 75 (2012), 3218-3228) and many others are extended and generalized to the class of ordered partial metric spaces.
276
292
Manish
Jain
Neetu
Gupta
Calogero
Vetro
Sanjay
Kumar
Coupled fixed point
Partial metric space
Contractions
Mixed monotone property.
Article.7.pdf
[
[1]
V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings partially ordered metric spaces, Nonlinear Anal. , 74 (2011), 7347-7355
##[2]
V. Berinde, Coupled fixed point theorems for \(\phi\)-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. , 75 (2012), 3218-3228
##[3]
S. G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and applications, in: Ann. New York Acad. Sci., 728 (1994), 183-197
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O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol. , 6 (2005), 229-240
##[5]
S. Oltra, O. Valero , Banach’s fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste , 36 (2004), 17-26
##[6]
I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl. , 157 (2010), 2778-2785
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. , 132 (2004), 1435-1443
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J. J. Nieto, R. R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) , 23 (12) (2007), 2205-2212
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R. P. Agarwal, M. A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces , Appl. Anal. , 87 (2008), 1-8
##[10]
I. Altun, H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. Article ID 621469 , 2010 (2010), 1-17
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J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. , 72 (2010), 1188-1197
##[12]
Z. Kadelburg, M. Pavlović, S. Radenović, Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl., 59 (2010), 3148-3159
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S. Radenović, Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. , 60 (2010), 1776-1783
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W. Sintunavarat, Y. J. Cho, P. Kumam, Common fixed point theorems for c-distance in ordered cone metric spaces, Comput. Math. Appl. , 62 (2011), 1969-1978
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T. G. Bhaskar, V. Lakshmikantham , Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
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N. V. Luong, N. X. Thuan, Coupled fixed point in partially ordered metric spaces and applications, Nonlinear Anal. , 74 (2011), 983-992
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I. Altun, A. Erdran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., Article ID 508730, 2010 (2010), 1-10
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I. Altun, H. Simsek, Some fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud. , 1 (2008), 1-8
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H. Aydi, Some coupled fixed point results on partial metric spaces, Int. J. Math. Math. Sci. Article ID 647091, , 2011 (2011), 1-11
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E. Karapinar, Weak \(\phi\)-contarction on partil contraction and existence of fixed points in partilally orederd sets, Math. Aeterna , 1 (4) (2011), 237-244
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B. Samet, M. Rajovi𝑐𝑐́, R. Lazovi𝑐𝑐́, R. Stojiljkovi𝑐𝑐́, Common fixed point results for nonlinear contractions in ordered partial metric spaces, Fixed Point Theory Appl. , (2011)
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W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling , 55 (2012), 680-687
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Prefunctions and System of Differential Equation Via Laplace Transform
Prefunctions and System of Differential Equation Via Laplace Transform
en
en
The purpose of this paper is to study the system of Linear Differential Equations of first order, Second order and Third order in two variables as well as in three variables and obtained the set of Pre-functions and extended prefunctions are the closed form of solutions via Laplace Transforms technique.
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D. B.
Dhaigude
S. B.
Dhaigude
Pre-functions
Extended prefunctions
Initial Value Problems and Laplace Transforms
Article.8.pdf
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