]>
2019
19
3
74
Null controllability of fractional stochastic delay integro-differential equations
Null controllability of fractional stochastic delay integro-differential equations
en
en
Sufficient conditions for exact null controllability of semilinear fractional stochastic delay integro-differential equations in Hilbert space are established. The required results are obtained based on fractional calculus, semigroup theory, Schauder's fixed point theorem and stochastic analysis.
In the end, an example is given to show the application of our results.
143
150
Hamdy M.
Ahmed
Higher Institute of Engineering
El-Shorouk Academy
Egypt
hamdy_17eg@yahoo.com
Mahmoud M.
El-Borai
Department of Mathematics, Faculty of Science
Alexandria University
Egypt
m_m_elborai@yahoo.com
H. M.
El-Owaidy
Department of Mathematics, Faculty of Science
Al-Azhar University
Egypt
elowaidy@yahoo.com
A. S.
Ghanem
Higher Institute of Engineering
El-Shorouk Academy
Egypt
ahmed.samir20134@gmail.com
Fractional calculus
null controllability
fractional stochastic delay integrodifferential equation
Schauder's fixed point theorem
Article.1.pdf
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O. Abu Arqub, M. Al-Smadi, Atangana--Baleanu fractional approach to the solutions of Bagley--Torvik and Painlevé equations in Hilbert space, Chaos Solitons Fractals, 117 (2018), 161-167
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O. Abu Arqub, M. Al-Smadi, Numerical algorithm for solving time--fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions, Numer. Methods Partial Differential Equations, 34 (2018), 1577-1597
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O. Abu Arqub, B. Maayah, Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana--Baleanu fractional operator, Chaos Solitons Fractals, 117 (2018), 117-124
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O. Abu Arqub, Z. Odibat, M. Al-Smadi, Numerical solutions of time--fractional partial integrodifferential equations of Robin functions types in Hilbert space with error bounds and error estimates, Nonlinear Dyn., 94 (2018), 1819-1834
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H. M. Ahmed, Controllability of fractional stochastic delay equations, Lobachevskii J. Math., 30 (2009), 195-202
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H. M. Ahmed, On some fractional stochastic integrodifferential equations in Hilbert spaces, Int. J. Math. Math. Sci., 2009 (2009), 1-8
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H. M. Ahmed, Approximate controllability of impulsive neutral stochastic differential equations with fractional Brownian motion in a Hilbert space, Adv. Difference Equ., 2014 (2014), 1-11
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H. M. Ahmed, M. M. El-Borai, Hilfer fractional stochastic integro-differential equations, Appl. Math. Comput., 331 (2018), 182-189
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A. Ali, B. Samet, K. Shah, R. A. Khan, Existence and stability of solution to a toppled systems of differential equations of non-integer order, Bound. Value Probl., 2017 (2017), 1-13
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A. Ali, K. Shah, R. A. Khan, Existence of solution to a coupled system of hybrid fractional differential equations, Bull. Math. Anal. Appl., 9 (2017), 9-18
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M. Al-Smadi, O. A. Arqub, Computational algorithm for solving fredholm time--fractional partial integrodifferential equations of dirichlet functions type with error estimates, Appl. Math. Comput., 342 (2019), 280-294
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P. Kumama, A. Ali, K. Shah, R. A. Khan, Existence results and Hyers--Ullam stability to a class of nonlinear arbitrary order differential equations, J. Nonlinear Sci. Appl., 2017 (2017), 2986-2997
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]
New scheme for nonlinear Schrödinger equations with variable coefficients
New scheme for nonlinear Schrödinger equations with variable coefficients
en
en
This paper proposes a numerical scheme for nonlinear Schrödinger equations with periodic variable coefficients and stochastic perturbation. The scheme is obtained by applying finite element method in spatial direction and finite difference scheme in temporal direction, respectively. The scheme is stable in the sense that it preserves discrete charge of the Schrödinger equations. The numerical examples verify the conservative property of the new scheme.
151
157
Xiu-Ling
Yin
School of Mathematical Sciences
Dezhou University
China
yinllmm@163.com
Shu-Xia
Kong
School of Mathematical Sciences
Dezhou University
China
Yan-Qin
Liu
School of Mathematical Sciences
Dezhou University
China
Xiao-Tong
Zheng
School of Statistics
Renmin University of China
China
Schrödinger equation
finite element method
finite difference scheme
Article.2.pdf
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]
The Gopala-Hemachandra universal code determined by straight lines
The Gopala-Hemachandra universal code determined by straight lines
en
en
Variation on the Fibonacci universal code, known as Gopala-Hemachandra (or GH) code, is mainly used in data compression and cryptography as it is a self-synchronizing code. In 2010, Basu and Prasad showed that Gopala-Hemachandra code \(GH_a(n)\) exists for \(-20 \leq a \leq -2\) and \(1 \leq n \leq 100\) as well as there are \(m\) consecutive non-existing Gopala-Hemachandra codewords in \(GH_{-(4+m)}(n)\) column where \(1 \leq m \leq 16\). In this paper, we have introduced GH code straight line in two-dimensional space where each integral point \((a, n)\) on the GH code straight line represents a unique GH codeword. GH code straight lines confirm the existence of GH codewords for any integer \(n \geq 1\) and integer \(a \leq -2\). Moreover, for a given parameter \((a, n)\), we have introduced two methods to check whether GH codeword exists or not.
158
170
Joydeb
Pal
Department of Mathematics
National Institute of Technology Durgapur
India
joydebpal77@gmail.com
Monojit
Das
Shibpur Dinobundhoo Institution (College)
India
monojitbhu@gmail.com
Fibonacci numbers
Fibonacci coding
Gopala-Hemachandra sequence
Gopala-Hemachandra code
Zeckendorf's representation
Article.3.pdf
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M. Basu, B. Prasad, Long range variations on the Fibonacci universal code, J. Number Theory, 130 (2010), 1925-1931
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]
Weighted Jessen's functionals and exponential convexity
Weighted Jessen's functionals and exponential convexity
en
en
In this paper, we give a refinement of the well known Jessen's
inequality via weight functions. We discuss \(m\)-exponential
convexity of the functions associated with these weighted Jessen's
functionals. Cauchy and Lagrange mean value theorems are also given
that are useful in the construction of means with Stolarsky
property.
171
180
Rishi
Naeem
School of Natural Sciences
National University of Sciences and Technology
Pakistan
rishi.naeem@sns.nust.edu.pk
Matloob
Anwar
School of Natural Sciences
National University of Sciences and Technology
Pakistan
manwar@sns.nust.edu.pk
Convex function
Jessen's inequality
log-convex functions
exponentially convex function
mean value theorems
Stolarsky means
Article.4.pdf
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]
The \(r\)-Bell numbers and matrices containing non-central Stirling and Lah numbers
The \(r\)-Bell numbers and matrices containing non-central Stirling and Lah numbers
en
en
In this paper, two new explicit formulas for \(r\)-Bell numbers are established. One formula is expressed in terms of \(r\)-Stirling numbers of the second kind and \(r\)-Lah numbers. The other formula is expressed in terms of the non-central Stirling numbers of the second kind and the ordinary Lah numbers. Moreover, some matrix relations are obtained involving \(r\)-Bell numbers, \(r\)-Stirling numbers of the second kind, \(r\)-Lah numbers, non-central Stirling numbers of the second kind, and the
ordinary Lah numbers.
181
191
Roberto B.
Corcino
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
rcorcino@yahoo.com
Cristina B.
Corcino
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
cristinacorcino@yahoo.com
Jeneveb T.
Malusay
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
ferdiemalusay@yahoo.com
Gaea Iolanthe Mari R.
Bercero
Research Institute for Computational Mathematics and Physics
Cebu Normal University
Philippines
gimbercero@gmail.com
\(r\)-Bell numbers
\(r\)-Stirling numbers
non-central Stirling numbers
\(r\)-Lah numbers
Lah numbers
Article.5.pdf
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K. N. Boyadzhiev, Lah Numbers, Laguerre Polynomials of Order Negative One, and the $n$th Derivative of $\exp(1/x)$, Acta Univ. Sapientiae Math., 8 (2016), 22-31
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S. Daboul, J. Mangaldan, M. Z. Spivey, P. J. Taylor, The Lah numbers and the $n$--th derivative of $e^{{1}/{x}}$, Math. Mag., 86 (2013), 39-47
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F. Qi, An explicit formula for the Bell numbers in terms of Lah and Stirling numbers, Mediterr. J. Math., 13 (2016), 2795-2800
]
Characterization of Marshall-Olkin-G family of distributions by truncated moments
Characterization of Marshall-Olkin-G family of distributions by truncated moments
en
en
In this paper, a characterization of the Marshall-Olkin-G family of distribution (MO-G)
[A. W. Marshall, I. Olkin, Biometrika, \(\bf 84\) (1997), 641--652] by left and right truncated moments based on a certain continuous function of a random variable is discussed under some necessary condition. We provide characterization of Marshall-Olkin Nadarajah-Haghighi distribution (MONH) [A. J. Lemonte, G. M. Cordeiro, G. Moreno-Arenas, Statistics, \(\bf 50\) (2016), 312--337] and Marshall-Olkin generalized Erlang-truncated exponential distribution (MOGETE) [I. E. Okorie, A. C. Akpanta, J. Ohakwe, Cogent Math., \(\bf 4\) (2017), 19 pages] for illustration.
192
202
Mustapha
Muhammad
College of Mathematics and Information Science
Hebei Normal University
China
mmuhammad.mth@buk.ed.ng
Lixia
Liu
College of Mathematics and Information Science
Hebei Normal University
China
liulixia@hebtu.edu.cn
MO-G family
MONH model
MOGETE model
truncated Moments
failure rate
reverse failure rate
characterization of distribution
Article.6.pdf
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[1]
M. Ahsanullah, M. E. Ghitany, D. K. Al-Mutairi, Characterization of Lindley distribution by truncated moments, Comm. Statist. Theory Methods, 46 (2017), 6222-6227
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A. Y. Al-Saiari, L. A. Baharith, S. A. Mousa, Marshall--Olkin extended Burr Type XII distribution, Int. J. Statist. Prob., 3 (2014), 78-84
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M. Javed, T. Nawaz, M. Irfan, The Marshall--Olkin kappa distribution: properties and applications, J. King Saud Uni. Sci., 2018 (2018), 1-10
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N. M. Kilany, Characterization of Lindley Distribution Based on Truncated Moments of Order Statistics, J. Statist. Appl. Prob., 6 (2017), 355-360
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A. W. Marshall, I. Olkin, A new method for adding a parameter to a family of distributions with application to the exponential and Weibull families, Biometrika, 84 (1997), 641-652
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M. Muhammad, L. Liu, A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data, Entropy, 21 (2019), 1-37
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I. E. Okorie, A. C. Akpanta, J. Ohakwe, Marshall--Olkin generalized Erlang--truncated exponential distribution: Properties and applications, Cogent Math., 4 (2017), 1-19
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]
Solving system of partial differential equations using variational iteration method with He's polynomials
Solving system of partial differential equations using variational iteration method with He's polynomials
en
en
In the present work, variational iteration method with He's polynomials (VIMHP) is widely proposed to elucidate the linear and nonlinear system of partial differential equations. In the proposed method, variational iteration method is coupled with homotopy perturbation methods using He's polynomials to handle the nonlinear terms. We emphasize the efficiency of this approach by solving two appropriate examples. The significant results for solving the linear and nonlinear coupled system of equations demonstrate the superiority and competence of this approach. The proposed method finds the solution without any restrictive assumptions, discretization, and linearization.
203
211
Muhammad
Nadeem
School of Mathematical Sciences
Dalian University of Technology
China
nadeem@mail.dlut.edu.cn
Shao-Wen
Yao
School of Mathematics and Information Science
Henan Polytechnic University
China
yaoshaowen@hpu.edu.cn
Coupled pseudo-parabolic equation
coupled Burgers equation
Lagrange multiplier
He's polynomials
Article.7.pdf
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M. A. Abdou, A. A. Soliman, Variational iteration method for solving Burger's and coupled Burger's equations, J. Comput. Appl. Math., 181 (2005), 245-251
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M. A. Al-Jawary, G. H. Radhi, J. Ravnik, Daftardar-Jafari method for solving nonlinear thin film flow problem, Arab J. Basic Appl. Sci., 25 (2018), 20-27
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N. Anjum, J.-H. He, Laplace transform: Making the variational iteration method easier, Appl. Math. Lett., 92 (2019), 134-138
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A. Daga, V. H. Pradhan, Variational homotopy perturbation method for solving nonlinear reaction--diffusion convection problems, Int. J. Adv. Engg. Res. Studies, 2 (2013), 11-14
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J.-H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals, 26 (2005), 695-700
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Dynamics of some parametric operators from the class of \( \zeta^{(as)}\)-QSO
Dynamics of some parametric operators from the class of \( \zeta^{(as)}\)-QSO
en
en
In this paper the quadratic stochastic operators (QSO) were considered, these operators describe the population dynamic system. Some quadratic stochastic operators were studied by Lotka and Volterra. Moreover, we discuss the dynamic of some parametric operators from the class of \( \zeta^{(as)}\)-QSO.
212
217
Basma M.
Al-Shutnawi
Department of Mathematics, Faculty of Science
Tafila Technical University
Jordan
basma@ttu.edu.jo
Quadratic stochastic operators
\(\zeta^{(as)}\)-QSO
fixed points
Article.8.pdf
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