]>
2020
13
4
ISSN 2008-1898
46
On the solution of Wave-Schrodinger equation
On the solution of Wave-Schrodinger equation
en
en
In this paper, we are finding a solution of the fractional Wave-Schrodinger equation by Laplace transform in the sense of Caputo fractional derivative. It was found that
the fundamental solution of the equation is related to Wright function.
176
179
Wanchak
Satsanit
Department of Mathematics, Faculty of Science
Maejo University
Thailand
wanchack@gmail.com
Dirac delta distribution
Laplacian operator
Wright function
Article.1.pdf
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A. Kananthai, On the Solution of the n-Dimensional Diamond Operator, Appl. Math. Comput., 88 (1997), 27-37
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A. Kananthai, S. Suantai, V, Longani, On the operator $\oplus^{k}$ related to the wave equation and Laplacian, Appl. Math. Comput., 132 (2002), 219-229
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I. Podlubny, Fractional Differential Equations, Acedemic Press, San Diego (1999)
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L. G. Romero, A generalization of the Laplacian operator, Palest. J. Math., 5 (2016), 204-207
]
Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach
Existence of integrable solutions for integro-differential inclusions of fractional order; coupled system approach
en
en
In this article, we establish the existence of solutions for a functional integral equation of fractional order.
The study upholds the case when the set-valued function has \(L^1\)-Caratheodory selections, we reformulate the functional integral inclusion according to these selections via a classical fixed point theorem of Schauder and present theorem for the existence of integrable solutions.
As an application, the existence of solutions of nonlinear functional integro-differential inclusion with an initial value,
and the initial value problem for the arbitrary-order differential inclusion will be studied.
180
186
A. M. A.
El-Sayed
Faculty of Science
Alexandria University
Egypt
amasayed@alexu.edu.eg
Sh. M.
Al-Issa
Faculty of Science
Faculty of Science
Lebanes International University
The International University of Beirut
Lebanon
Lebanon
shorouk.alissa@liu.edu.lb
Fractional calculus
integro-differential inclusion
\(L^1\)-Caratheodory selections
Schauder fixed point principle
Kolmogorov compactness criterion
Article.2.pdf
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[1]
S. Al-Issa, A. M. A. El-Sayed, Positive integrable solutions for nonlinear integral and differential inclusions of fractional-orders, Comment. Math., 49 (2009), 171-177
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J.-P. Aubin A. Cellina, Differential Inclusion, Springer-Verlag, Berlin (1984)
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A. M. A. El-Sayed, S. M. Al-Issa, Existence of continuous solutions for nonlinear functional differential and integral inclusions, Malaya J. Mat., 7 (2019), 541-544
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A. M. A. El-Sayed, S. M. Al-Issa, Monotonic integrable solution for a mixed type integral and differential inclusion of fractional orders, Int. J. Differ. Equations Appl., 18 (2019), 1-10
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A. M. A. El-Sayed, S. M. Al-Issa, Monotonic solutions for a quadratic integral equation of fractional order, AIMS Mathematics, 4 (2019), 821-830
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K. Kuratowski, C. Ryll-Nardzewski, Ageneral theorem on selectors, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 13 (1965), 397-403
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D. O'Regan, Integral inclusions of upper semi-continuous or lower semi-continuous type, Proc. Amer. Math. Soc., 124 (1996), 2391-2399
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S. G. Samko, A. A. Kilbas, O. I. Marichev, Integrals and Derivatives of Fractional Orders and Some of their Applications, Nauka i Teknika, Minsk (1987)
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]
Stability, controllability, and observability criteria for state-space dynamical systems on measure chains with an application to fixed point arithmetic
Stability, controllability, and observability criteria for state-space dynamical systems on measure chains with an application to fixed point arithmetic
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en
In this paper, our main attempt is to unify results on stability, controllability, and observability criteria on real-time dynamical systems with non-uniform domains. The results of continuous/discrete systems will now become a particular case of our results. As an application a first-order time scale dynamical system on measure chains in one-dimensional state space having both continuous/discrete filters to minimize the effect of a round of noise at the filter outputs is presented. A set of necessary and sufficient conditions for this dynamical system to be stable and completely stable are established.
187
195
Yan
Wu
Department of Mathematical Sciences
Georgia Southern University
USA
Sailaja
P
Department of Mathematics
Geethanjali Engineering College
India
K. N.
Murty
Department of Applied Mathematics
Andhra University
India
nkanuri@hotmail.com
Linear Systems
time scale dynamical systems
control systems
concurrency control
Article.3.pdf
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B. Aulbach, S. Hilger, A unified Approach to Continuous and Discrete Dynamics, Qualitative theory of differential equations (Szeged), 1988 (1988), 37-56
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B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale, Nonlinear dynamics and quantum dynamical systems (Gaussig), 1990 (1990), 9-20
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K. V. V. Kanuri, , R. Suryanarayana, K. N. Murty, Existence of $\Psi$-bounded solutions for linear differential systems on time scales, J. Math. Comput. Sci., 20 (2020), 1-13
##[6]
V. Lakshmikantham, S. Sivasundaram, B. Kaymakcalan, Dynamic systems on measure chains, Kluwer Academic Publishers Group, Dordrecht (1996)
##[7]
H. J. Ko, Stability Analysis of Digital Filters Under Finite Word Length Effects via Normal-Form Transformation, Asian J. Health Infor. Sci., 1 (2006), 112-121
##[8]
K. N. Murty, Y. Wu, V. Kanuri, Metrics that suit for dichotomy, well conditioning and object oriented design on measure chains, Nonlinear Stud., 18 (2011), 621-637
]
Some fixed point theorems in fuzzy bipolar metric spaces
Some fixed point theorems in fuzzy bipolar metric spaces
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en
In this paper, we introduce the notion of fuzzy bipolar metric space and prove some fixed point results in this space. We provide some non-trivial examples to support our claim and also give applications for the usability of the main result in fuzzy bipolar metric spaces.
196
204
Ayush
Bartwal
Department of Mathematics
HNB Garhwal University
India
ayushbartwal@gmail.com
R. C.
Dimri
Department of Mathematics
HNB Garhwal University
India
dimrirc@gmail.com
Gopi
Prasad
Department of Mathematics
HNB Garhwal University
India
gopiprasad127@gmail.com
Fuzzy metric spaces
fuzzy bipolar metric space
fixed point
Article.4.pdf
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G. N. V. Kishore, R. P. Agarwal, B. Srinuvasa Rao, R. V. N. Srinuvasa Rao, Caristi type cyclic contraction and common fixed point theorems in bipolar metric spaces with applications, Fixed Point Theory Appl., 2018 (2018), 1-13
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A. Mutlu, K. Özkan, U. Gürdal, Fixed point theorems for multivalued mapping on bipolar metric spaces, Fixed Point Theory, (), -
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]
A fixed point method to solve differential equation and Fredholm integral equation
A fixed point method to solve differential equation and Fredholm integral equation
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en
The purpose of this research is to explore a fixed point method to solve a class of functional equations, \(Tu=f\), where \(T\) is a differential or an integral operator on a Sobolev space \(H^2(\Omega)\), where \(\Omega\) is an open set in \(\mathbb{R}^n\). First, \(T\) is converted into a sum of \(I+\lambda A\) with \(\lambda>0\), where \(A\) is a continuous linear operator and \(I\) is identity mapping. Then it is shown that \(T\) is a contraction on the prescribed Sobolev space and norm of \(A\) is estimated on the prescribed Sobolev space. By means of the theory of inverse operator of \(I+\lambda A\) and by choosing the appropriate value of \(\lambda\), the solution \(u\) of differential or integral operator is obtained. Some practical problems concerning the linear differential equation and Fredholm integral equation are solved by virtue of the fixed point method.
205
211
Ei Ei
Nyein
School of Mathematics and Statistics
Beijing Institute of Technology
China
eieinyein1985@yahoo.com
Aung Khaing
Zaw
School of Mathematics and Statistics
Beijing Institute of Technology
China
akzbee451986@yahoo.com
Fixed point method
ODE and PDE
Fredholm integral equation
estimation
Article.5.pdf
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M. A. Alghamdi1, W. A. Kirk, N. Shahzad, Metric fixed point theory for nonexpansive mappings defined on unbounded sets, Fixed Point Theory Appl., 2014 (2014), 1-12
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M. M. El-Borai, W. G. El-Sayed, N. N. Khalefa, Solvability of Some Nonlinear Integral Functional Equations, Amer. J. Theor. Appl. Stat., 6 (2017), 13-22
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A. P. Farajzadeh, A. Kaewcharoen, S. Plubtieng, An Application of Fixed Point Theory to a Nonlinear Differential Equation, Abstr. Appl. Anal., 2014 (2014), 1-7
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]
Generalized Suzuki type \( \alpha \)-\( \mathcal{Z} \)-contraction in b-metric space
Generalized Suzuki type \( \alpha \)-\( \mathcal{Z} \)-contraction in b-metric space
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en
In this paper, we introduce the concept of generalized Suzuki type \(\alpha\)-\( \mathcal{Z} \)-contraction concerning a simulation function \(\zeta\) in b-metric space and prove the existence of fixed point results for this contraction. Our result extend the fixed point result of [A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya, Kragujevac J. Math., \(\bf 42\) (2018), 419--430].
212
222
Swati
Antal
Department of Mathematics
H.N.B. Garhwal University
India
antalswati11@gmail.com
U. C.
Gairola
Department of Mathematics
H.N.B. Garhwal University
India
ucgairola@rediffmail.com
Simulation function
triangular \(\alpha\)-admissible mapping with respect to \(\zeta\) \sep b-metric space
generalized Suzuki type \(\alpha\)-\( \mathcal{Z} \)-contraction mapping
Article.6.pdf
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H. Aydi, M. Jellali, E. Karapinar, On fixed point results for $\alpha$-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21 (2016), 40-56
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G. V. R. Babu, D. T. Mosissa, Fixed point in $b$-metric space via simulation function, Novi Sad J. Math., 47 (2017), 133-147
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M. Boriceanu, Strict fixed point theorems for multivalued operators in $b$-metric space, Int. J. Mod. Math., 4 (2009), 285-301
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E. Karapinar, P. Kumam, P. Salimi, On $\alpha$-$\psi$-Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12
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F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189-1194
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P. Kumam, D. Gopal, L. Budhia, A new fixed point theorem under Suzuki type $Z$-contraction mappings, J. Math. Anal., 8 (2017), 113-119
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B. Mohammadi, S. Rezapour, N. Shahzad, Some results on fixed points of $\alpha$-$\psi$-Ciric generalized multifunctions, Fixed Point Theory Appl., 2013 (2013), 1-10
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M. Pacurar, Sequences of almost contractions and fixed points in $b$-metric spaces, An. Univ. Vest Timiş. Ser. Mat.-Inform., 48 (2010), 125-137
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A. Padcharoen, P. Kumam, P. Saipara, P. Chaipunya, Generalized Suzuki type $\mathcal{Z}$-contraction in complete metric spaces, Kragujevac J. Math., 42 (2018), 419-430
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J. R. Roshan, V. Parvaneh, Z. Kadelberg, Common fixed point theorems for weakly isotone increasing mappings in ordered $b$-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229-245
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]