• Title/Summary/Keyword: Nonlocal condition

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FRACTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL BOUNDARY CONDITIONS

  • Soenjaya, Agus L.
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.497-502
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    • 2022
  • Existence and uniqueness for fractional differential equations satisfying a general nonlocal initial or boundary condition are proven by means of Schauder's fixed point theorem. The nonlocal condition is given as an integral with respect to a signed measure, and includes the standard initial value condition and multi-point boundary value condition.

Existence and Uniqueness of Solutions for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory

  • Kwun, Young-Chel;Park, Jong-Seo;Kim, Seon-Yu;Park, Jin-Han
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.6 no.4
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    • pp.288-292
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    • 2006
  • Many authors have studied several concepts of fuzzy systems. Balasubramaniam and Muralisankar (2004) proved the existence and uniqueness of fuzzy solutions for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. Recently, Park, Park and Kwun (2006) find the sufficient condition of nonlocal controllability for the semilinear fuzzy integrodifferential equation with nonlocal initial condition. In this paper, we study the existence and uniqueness of solutions for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_{N}$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_{N}$.

SOME TYPES OF REACTION-DIFFUSION SYSTEMS WITH NONLOCAL BOUNDARY CONDITIONS

  • Han, Yuzhu;Gao, Wenjie
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.6
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    • pp.1765-1780
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    • 2013
  • This paper deals with some types of semilinear parabolic systems with localized or nonlocal sources and nonlocal boundary conditions. The authors first derive some global existence and blow-up criteria. And then, for blow-up solutions, they study the global blow-up property as well as the precise blow-up rate estimates, which has been seldom studied until now.

Effect of dimensionless nonlocal parameter: Vibration of double-walled CNTs

  • Hussain, Muzamal;Asghar, Sehar;Khadimallah, Mohamed Amine;Ayed, Hamdi;Alghamdi, Sami;Bhutto, Javed Khan;Mahmoud, S.R.;Tounsi, Abdelouahed
    • Computers and Concrete
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    • v.30 no.4
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    • pp.269-276
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    • 2022
  • In this paper, frequency vibrations of double-walled carbon nanotubes (CNTs) has been investigated based upon nonlocal elastic theory. The inference of small scale is being perceived by establishing nonlocal Love shell model. The wave propagation approach has been operated to frame the governing equations as eigen value system. An innovational nonlocal model to examine the scale effect on vibrational behavior of armchair, zigzag and chiral of double-walled CNTs. An appropriate selection of material properties and nonlocal parameter has been considered. The influence of dimensionless nonlocal parameter has been studied in detail. The dominance of end condition via nonlocal parameter is explained graphically. The results generated furnish the evidence regarding applicability of nonlocal shell model and also verified by earlier published literature.

PROPERTIES OF POSITIVE SOLUTIONS FOR A NONLOCAL REACTION-DIFFUSION EQUATION WITH NONLOCAL NONLINEAR BOUNDARY CONDITION

  • Mu, Chunlai;Liu, Dengming;Zhou, Shouming
    • Journal of the Korean Mathematical Society
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    • v.47 no.6
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    • pp.1317-1328
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    • 2010
  • In this paper, we study the properties of positive solutions for the reaction-diffusion equation $u_t$ = $\Delta_u+{\int}_\Omega u^pdx-ku^q$ in $\Omega\times(0,T)$ with nonlocal nonlinear boundary condition u (x, t) = ${\int}_{\Omega}f(x,y)u^l(y,t)dy$ $\partial\Omega\times(0,T)$ and nonnegative initial data $u_0$ (x), where p, q, k, l > 0. Some conditions for the existence and nonexistence of global positive solutions are given.