Picard iterative processes for initial value problems of singular fractional differential equations
, 2014 In this paper, the initial value problems of singular fractional differential equations are discussed. New criteria on the existence and uniqueness of solutions are obtained.
Xiaohui Yang, Yuji Liu
semanticscholar +1 more source
An investigation of fractional Bagley-Torvik equation
Open Mathematics, 2019 In this paper the authors prove the existence as well as approximations of the solutions for the Bagley-Torvik equation admitting only the existence of a lower (coupled lower and upper) solution.
Fazli Hossein, Nieto Juan J.
doaj +1 more source
On solvability of an indefinite Riccati equation [PDF]
, 2013 This note concerns a class of matrix Riccati equations associated with stochastic linear-quadratic optimal control problems with indefinite state and control weighting costs. A novel sufficient condition of solvability of such equations is derived, based
Du, Kai
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A Closed-Form Solution to the Arbitrary Order Cauchy Problem with Propagators [PDF]
, 2014 The general abstract arbitrary order (N) Cauchy problem was solved in a closed form as a sum of exponential propagator functions. The infinite sparse exponential series was solved with the aid of a homogeneous differential equation. It generated a linear
Stenlund, Henrik
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On the local structure of the Klein-Gordon field on curved spacetimes [PDF]
, 2000 This paper investigates wave-equations on spacetimes with a metric which is locally analytic in the time. We use recent results in the theory of the non-characteristic Cauchy problem to show that a solution to a wave-equation vanishing in an open set ...
Strohmaier, Alexander
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An Analytical Framework to Describe the Interactions Between Individuals and a Continuum
, 2010 We consider a discrete set of individual agents interacting with a continuum. Examples might be a predator facing a huge group of preys, or a few shepherd dogs driving a herd of sheeps.
A. Bressan +14 more
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SOLVING FRACTIONAL INTEGRO DIFFERENTIAL EQUATIONS BY HOMOTOPY ANALYSIS TRANSFORM METHOD
, 2016 In this paper, we introduce an analytical method, which so called the homotopy analysis transform method (HATM) which is a combination of HAM and Laplace decomposition method (LDM).
M. Mohamed, M. Alharthi, R. A. Alotabi
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Existence of Solutions for Nonconvex Differential Inclusions of Monotone Type [PDF]
, 2013 Differential inclusions with compact, upper semi-continuous, not necessarily convex right-hand sides in R^n are studied. Under a weakened monotonicity-type condition the existence of solutions is proved.Comment: 5 pages, 14 ...
Baier, Robert +2 more
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FLOW WITH $A_{\infty }(\mathbb{R})$ DENSITY AND TRANSPORT EQUATION IN $\text{BMO}(\mathbb{R})$
Forum of Mathematics, Sigma, 2019 We show that, if $b\in L^{1}(0,T;L_{\operatorname{loc}}^{1}(\mathbb{R}))$ has a spatial derivative in the John–Nirenberg space $\operatorname{BMO}(\mathbb{R})$, then it generates a unique flow $\unicode[STIX]{x1D719}(t,\cdot )$ which has an $A_{\infty }(\
RENJIN JIANG, KANGWEI LI, JIE XIAO
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Radial transonic shock solutions of Euler-Poisson system in convergent nozzles
, 2017 Given constant data of density $\rho_0$, velocity $-u_0{\bf e}_r$, pressure $p_0$ and electric force $-E_0{\bf e}_r$ for supersonic flow at the entrance, and constant pressure $p_{\rm ex}$ for subsonic flow at the exit, we prove that Euler-Poisson system
Bae, Myoungjean, Park, Yong
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