Discontinuous Parabolic Problems with a Nonlocal Initial Condition [PDF]
Boundary Value Problems, 2011 We study parabolic differential equations with a discontinuous nonlinearity and subjected to a nonlocal initial condition. We are concerned with the existence of solutions in the weak sense.
Boucherif Abdelkader
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Fractional parabolic problems with a nonlocal initial condition [PDF]
Moroccan Journal of Pure and Applied Analysis, 2017 In this work we will consider a class of non local parabolic problems with nonlocal initial condition, more precisely we deal with the ...
Abdellaoui B. +2 more
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A note on the fractional Cauchy problems with nonlocal initial conditions [PDF]
Applied Mathematics Letters, 2011 The authors consider the Cauchy problem \[ D^\beta_t u(t)+ Au(t)= f(t,u(t))+ \int^t_0 K(t-s) g(s,u(s))\,ds,\quad t\in [0,T], \] with \(u(0)= H(u)\). Here \(D^\beta_t\) is a fractional time derivative of order \(\beta\in(0, 1)\), \(-A\) generates a compact analytic semigroup \(T(t)\) on a Banach space \(X\), \(u\in C([0,T]; X_\alpha)\) (\(X_\alpha\) the
Jin Liang +2 more
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Solutions to Fractional Differential Equations with Nonlocal Initial Condition in Banach Spaces [PDF]
Advances in Difference Equations, 2010 A new existence and uniqueness theorem is given for solutions to differential equations involving the Caputo fractional derivative with nonlocal initial condition in Banach spaces. An application is also given.
Jin Liang, Zhi-Wei Lv, Ti-Jun Xiao
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Existence of solutions of generalized fractional differential equation with nonlocal initial condition [PDF]
Mathematica Bohemica, 2019 This paper is devoted to studying the existence of solutions of a nonlocal initial value problem involving generalized Katugampola fractional derivative.
Sandeep P. Bhairat +1 more
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Initial-boundary value problem with a nonlocal condition for a viscosity equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 This paper deals with the proof of the existence, uniqueness, and continuous dependence of a strong solution upon the data, for an initial-boundary value problem which combine Neumann and integral conditions for a viscosity equation.
Abdelfatah Bouziani
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First-order differential inclusions with nonlocal initial conditions
Applied Mathematics Letters, 2002 It is considered the following nonlocal initial value problem \[ x'(t)\in F(t,x(t)),\quad t\in (0,1],\qquad x(0)+\sum_{k=1}^{m}a_{k}x(t_{k})=x_{0}, \tag{1} \] where \(F:(0,1]\times \mathbb{R}\to 2^{\mathbb{R}}\) is a set-valued map, \(x_{0}\in \mathbb{R}\) is given ...
Abdelkader Boucherif
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Existence of Solutions to Fractional Mixed Integrodifferential Equations with Nonlocal Initial Condition [PDF]
Advances in Difference Equations, 2011 We study the existence and uniqueness theorem for the nonlinear fractional mixed Volterra-Fredholm integrodifferential equation with nonlocal initial condition , where , , and is a given function.
A. Anguraj +2 more
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Semilinear integrodifferential equations with nonlocal initial conditions
Computers and Mathematics With Applications, 2004 The paper is concerned with developing existence and uniqueness theorems for the Cauchy problem for semilinear integro-differential equations of convolution type. The sequence of theorems presented extends the existing results and can be applied, as is shown in the final section of the paper, to problems that arise in heat conduction in materials with ...
Jin Liang, Ti-Jun Xiao
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Controllability of semilinear boundary problems with nonlocal initial conditions
Journal of Mathematical Analysis and Applications, 2006 The authors consider a semilinear nonautonomous boundary problem with nonlocal initial conditions. First, they prove the existence of a mild solution of the problem by constructing a contractive map; the solution is given by a variation of constants formula. Ideas of preceeding papers (in press and preprint) are used.
L Maniar
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