]>
2019
12
9
ISSN 2008-1898
58
Stability analysis of the generalized fractional differential equations with and without exogenous inputs
Stability analysis of the generalized fractional differential equations with and without exogenous inputs
en
en
The stability conditions of the fractional differential equations described by the Caputo generalized fractional derivative have been addressed. The generalized asymptotic stability of a class of the fractional differential equations has been investigated. The fractional input stability in the context of the fractional differential equations described by the Caputo generalized fractional derivative has been introduced. The Lyapunov characterizations of the generalized asymptotic stability and the generalized fractional input stability of the fractional differential equations with or without inputs have been provided. Several examples illustrating the main results of the paper have been proposed. The Caputo generalized fractional derivative and the generalized Gronwall lemma have been used.
562
572
Ndolane
Sene
Laboratoire Lmdan, Departement de Mathematiques de la Decision
Universite Cheikh Anta Diop de Dakar
Senegal
ndolanesene@yahoo.fr
Caputo generalized fractional derivative
asymptotic stability
fractional differential equations
Article.1.pdf
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D. Baleanu, G.-C. Wu, S.-D. Zeng, Chaos analysis and asymptotic stability of generalized caputo fractional differential equations, Chaos Solitons Fractals, 102 (2017), 99-105
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N. Sene, Fractional input stability and its application to neural network, Discrete Contin. Dyn. Syst. Ser. S, 13 (2019), 853-865
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N. Sene, Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives, AIMS Math., 4 (2019), 147-165
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]
Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions
Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions
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en
We discuss the existence, uniqueness and continuous dependence of solution for a non-autonomous semilinear Hilfer fractional differential equation with nonlocal conditions in the space of weighted continuous functions. By means of the Krasnoselskii's fixed point theorem and the generalized Gronwall's inequality, we establish the desired results.
573
581
Mohamed I.
Abbas
Department of Mathematics and Computer Science, Faculty of Science
Alexandria University
Egypt
miabbas77@gmail.com
Hilfer fractional derivative
Krasnoselskii's fixed point theorem
Gronwall's inequality
Article.2.pdf
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]
Coincidence points of self mappings and left total relations
Coincidence points of self mappings and left total relations
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en
The aim of this article is to prove some coincidence and fixed point
theorems of hybrid contractions involving left total relations and
single-valued mappings in the setting of \(\mathcal{F}\)-metric spaces which
was first introduced by Jleli and Samet [M. Jleli, B. Samet, J. Fixed Point Theory Appl., \(\textbf{20}\) (2018), 20 pages]. Finally, an example is also presented to verify the effectiveness
and applicability of our main results.
582
588
Laila A.
Alnaser
Department of Mathematics, College of Science
Taibah University
Kingdom of Saudi Arabia
alnaser_layla@yahoo.com
Durdana
Lateef
Department of Mathematics, College of Science
Taibah University
Kingdom of Saudi Arabia
drdurdanamaths@gmail.com
Hoda A.
Fouad
Department of Mathematics, College of Science
Department of Mathematics and Computer Science, Faculty of Science
Taibah University
Alexandria University
Kingdom of Saudi Arabia
Egypt
hoda_rg@yahoo.com
Jamshaid
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jkhan@uj.edu.sa
\(\mathcal{F}\)-metric space
fixed point
rational contraction
Article.3.pdf
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A. Azam, Coincidence points of mappings and relations with applications, Fixed Point Theory Appl., 2012 (2012), 1-9
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S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133-181
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M. Jleli, B. Samet, On a new generalization of Metric Spaces, J. Fixed Point Theory Appl., 20 (2018), 1-20
]
Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth
Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth
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en
In the one-dimensional reaction-diffusion domain of this study, semi-analytical solutions are used for a delayed viral infection system with logistic growth. Through an ordinary differential equations system, the Galerkin technique is believed to estimate the prevailing partial differential equations. In addition, Hopf bifurcation maps are constructed. The effect of diffusion coefficient stricture and delay on the model is comprehensively investigated, and the outcomes demonstrate that diffusion and delay can stabilize or destabilize the system. We found that, as the delay parameter values rise, the values of the Hopf bifurcations for growth and the rates of viral death are augmented, whereas the rate of production is decreased. For the growth, production, and death rates strictures, there is determination of an asymptotically unstable region and a stable region. Illustrations of the unstable and stable limit cycles, as well as the Hopf bifurcation points, are found to prove the formerly revealed outcomes in the Hopf bifurcation map. The results of the semi-analytical solutions and numerical assessments revealed that the semi-analytical solutions are highly effective.
589
601
H. Y.
Alfifi
Department of Basic Sciences, College of Education
Imam Abdulrahman Bin Faisal University
Saudi Arabia
hyalfifi@iau.edu.sa
Reaction-diffusion
delay
Hopf bifurcations
viral infection
semi-analytical solutions
limit cycle
Article.4.pdf
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H. Y. Alfifi, Semi-analytical solutions for the delayed diffusive food-limited model, 7th International Conference on Modeling, Simulation, and Applied Optimization ICMSAO (Sharjah, U. A. E.), 2017 (2017), 1-5
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H. Y. Alfifi, T. R. Marchant, Feedback Control for a Diffusive Delay Logistic Equation: Semi-analytical Solutions, IAENG Int. J. Appl. Math., 48 (2018), 317-323
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N. C. Chi, E. AvilaVales, G. Garcia Almeida, Analysis of a HBV model with diffusion and time delay, J. Appl. Math., 2012 (2012), 1-25
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H. Miao, Z. D. Teng, X. Abdurahman, Z. M. Li, Global stability of a diffusive and delayed virus infection model with general incidence function and adaptive immune response, Comp. Appl. Math., 37 (2018), 3780-3805
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M. H. Qiao, H. Qi, Dynamics of the HBV Model with Diffusion and Time Delay, IEEE International Workshop on Chaos-Fractals Theories and Applications, 2009 (2009), 297-300
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]
Real fixed points and singular values of family of functions arising from generating function of unified generalized Apostol-type polynomials
Real fixed points and singular values of family of functions arising from generating function of unified generalized Apostol-type polynomials
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en
Our main objective is to study the real fixed points and singular values of a two-parameter family of transcendental meromorphic functions \(g_{\lambda,n}(z)=\lambda \frac{z}{(b^{z}-1)^{n}}\), \(\lambda \in \mathbb{R} \backslash \{0\}\), \(z \in \mathbb{C} \backslash \{0\}\), \(n\in \mathbb{N} \backslash \{1\}\), \(b>0\), \(b\neq 1\) in the present paper which obtains from generating function of the unified generalized Apostol-type polynomials. The real fixed points of \(g_{\lambda,n}(x)\), \(x\in {\mathbb{R}}\setminus \{0\}\) with their stability are found for \(n\) odd and \(n\) even. It is shown that \(g_{\lambda,n}(z)\) has infinite number of singular values. Further, it is seen that some critical values of \(g_{\lambda,n}(z)\) lie in the closure of the disk and other lie in the exterior of the disk with center at the origin.
602
610
Mohammad
Sajid
College of Engineering
Qassim University
Saudi Arabia
msajd@qu.edu.sa
Real fixed points
critical values
singular values
meromorphic function
Article.5.pdf
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M. Sajid, Singular Values of One Parameter Family $\lambda \frac{b^{z}-1}{z}$, J. Math. Comput. Sci., 15 (2015), 204-208
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M. Sajid, Singular values of one parameter family of generalized generating function of Bernoulli's numbers, Appl. Math. Inf. Sci., 9 (2015), 2921-2924
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M. Sajid, Real fixed points and dynamics of one parameter family of function $(b^{x}-1)/x$, J. Association Arab Uni. Basic Appl. Sci., 21 (2016), 92-95
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M. Sajid, Singular values of two parameter families $\lambda{\bigg(\dfrac{b^{z}-1}{z}}\bigg)^{\mu}$ and $\lambda{\bigg(\dfrac{z}{b^{z}-1}}\bigg)^{\eta}$, J. Taibah Uni. Sci., 11 (2017), 324-327
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M. Sajid, Bifurcation and chaos in real dynamics of a two-parameter family arising from generating function of generalized Apostol-type polynomials, Math. Comput. Appl., 23 (2018), 1-11
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M. Sajid, G. P. Kapoor, Chaos in dynamics of a family of transcendental meromorphic functions, J. Nonlinear Anal. Appl., 2017 (2017), 1-11
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S. Sharifi, M. Salimi, S. Siegmund, T. Lotfi, A new class of optimal four-point methods with convergence order 16 for solving nonlinear equations, Math. Comput. Simulation, 119 (2016), 69-90
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H. M. Srivastava, Some generalizations and basic (or $q-$) extensions of the Bernoulli, Euler and Genocchi polynomials, Appl. Math. Inf. Sci., 5 (2011), 390-444
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J. H. Zheng, On fixed-points and singular values of transcendental meromorphic functions, Sci. China Math., 53 (2010), 887-894
]
On the attractivity of an integrodifferential system with state-dependent delay
On the attractivity of an integrodifferential system with state-dependent delay
en
en
This work is focused on the existence and attractivity of mild solutions for an integrodifferential system with state-dependent delay. The results presented here were established by means of a fixed point theorem due to [T. A. Burton, C. Kirk, Math. Nachr., \(\bf189\) (1998), 23--31]. At the end, the obtained results are illustrated by an example.
611
620
Kora Hafiz
Bete
Universite d'Abomey-Calavi
Institut de Mathematiques et de Sciences Physiques
Benin
betekora.hafiz@imsp-uac.org
Carlos
Ogouyandjou
Universite d'Abomey-Calavi
Institut de Mathematiques et de Sciences Physiques
Benin
ogouyandjou@imsp-uac.org
Amadou
Diop
Universite Gaston Berger de Saint-Louis, UFR SAT
Departement de Mathematiques
Senegal
diop.amadou@ugb.edu.sn
Mamadou Abdoul
Diop
Universite Gaston Berger de Saint-Louis, UFR SAT
Departement de Mathematiques
Senegal
mamadou-abdoul.diop@ugb.edu.sn
Neutral functional integrodifferential equations
resolvent operator
mild solution
local attractivity
fixed point theory
infinite delay
Article.6.pdf
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K. Balachandran, R. R. Kumar, Existence of solutions of integrodifferential evolution equations with time varying delays, Appl. Math. E-Notes, 7 (2007), 1-8
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