THE SOLUTION OF EULER-CAUCHY EQUATION EXPRESSED BY DIFFERENTIAL OPERATOR USING LAPLACE TRANSFORM
, 2013 It is well known fact that the Laplace transform is useful in solving linear ordinary differential equations with constant coefficients such as free/forced oscillations, but in the case of differential equation with variable coefficients is not. In here,
H. Kim
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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, uniqueness and exponential boundedness of global solutions to delay fractional differential equations [PDF]
Mediterr. J. Math. 14 (2017), 2017 Under a mild Lipschitz condition we prove a theorem on the existence and uniqueness of global solutions to delay fractional differential equations. Then, we establish a result on the exponential boundedness for these solutions.
arxiv +1 more source
Existence and approximation of solutions of some first order iterative differential equations
, 2010 Existence theorems for some iterative differential equations as well as convergence theorems for a fixed point iterative method designed to approximate these solutions, are proved under weaker conditions than those due to A.
V. Berinde
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A uniqueness result on ordinary differential equations with singular coefficients [PDF]
arXiv, 2008 We consider the uniqueness of solutions of ordinary differential equations where the coefficients may have singularities. We derive upper bounds on the the order of singularities of the coefficients and provide examples to illustrate the results.
arxiv
, 2012 This article studies a new class of nonlocal boundary value problems of nonlinear differential equations and inclusions of fractional order with strip conditions.
B. Ahmad, S. Ntouyas
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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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Exponential ergodicity for SDEs with jumps and non-Lipschitz coefficients [PDF]
arXiv, 2012 In this paper we show irreducibility and the strong Feller property for transition probabilities of stochastic differential equations with jumps and monotone coefficients. Thus, exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained.
arxiv
, 2012 This article studies the existence and dimension of the set for mild solutions of semilinear fractional differential inclusions. We recall and prove some new results on multivalued maps to establish our main results.MSC 2010: 34A12; 34A40.
R. Agarwal +3 more
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On second-order linear Stieltjes differential equations with non-constant coefficients
Open MathematicsIn this work, we define the notions of Wronskian and simplified Wronskian for Stieltjes derivatives and study some of their properties in a similar manner to the context of time scales or the usual derivative.
Fernández Francisco J. +2 more
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