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Fractional virus epidemic model on financial networks

100%
Balci M. A.
Open Mathematics
|
2016
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tom 14
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nr 1
1074-1086
EN
In this study, we present an epidemic model that characterizes the behavior of a financial network of globally operating stock markets. Since the long time series have a global memory effect, we represent our model by using the fractional calculus. This model operates on a network, where vertices are the stock markets and edges are constructed by the correlation distances. Thereafter, we find an analytical solution to commensurate system and use the well-known differential transform method to obtain the solution of incommensurate system of fractional differential equations. Our findings are confirmed and complemented by the data set of the relevant stock markets between 2006 and 2016. Rather than the hypothetical values, we use the Hurst Exponent of each time series to approximate the fraction size and graph theoretical concepts to obtain the variables.
2
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Boundary value problems for differential inclusions with fractional order

100%
Benchohra M., Hamani S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2008
|
tom 28
|
nr 1
147-164
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
3
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Fractional BVPs with strong time singularities and the limit properties of their solutions

86%
Staněk S.
Open Mathematics
|
2014
|
tom 12
|
nr 11
1638-1655
EN
In the first part, we investigate the singular BVP $$\tfrac{d} {{dt}}^c D^\alpha u + (a/t)^c D^\alpha u = \mathcal{H}u$$, u(0) = A, u(1) = B, c D α u(t)|t=0 = 0, where $$\mathcal{H}$$ is a continuous operator, α ∈ (0, 1) and a < 0. Here, c D denotes the Caputo fractional derivative. The existence result is proved by the Leray-Schauder nonlinear alternative. The second part establishes the relations between solutions of the sequence of problems $$\tfrac{d} {{dt}}^c D^{\alpha _n } u + (a/t)^c D^{\alpha _n } u = f(t,u,^c D^{\beta _n } u)$$, u(0) = A, u(1) = B, $$\left. {^c D^{\alpha _n } u(t)} \right|_{t = 0} = 0$$ where a < 0, 0 < β n ≤ α n < 1, limn→∞ β n = 1, and solutions of u″+(a/t)u′ = f(t, u, u′) satisfying the boundary conditions u(0) = A, u(1) = B, u′(0) = 0.
4
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Fractional integro-differential inclusions with state-dependent delay

86%
Aissani K., Benchohra M., Ezzinbi K.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2014
|
tom 34
|
nr 2
153-167
EN
In this paper, we establish sufficient conditions for the existence of mild solutions for fractional integro-differential inclusions with state-dependent delay. The techniques rely on fractional calculus, multivalued mapping on a bounded set and Bohnenblust-Karlin's fixed point theorem. Finally, we present an example to illustrate the theory.
5
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Boundary Value Problems for Differential Equations with Fractional Order and Nonlinear Integral Conditions

86%
Benchohra M., Hamani S.
Commentationes Mathematicae
|
2009
|
tom 49
|
nr 2
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlinear integral conditions.
6
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Existence and stability analysis of nonlinear sequential coupled system of Caputo fractional differential equations with integral boundary conditions

86%
Zada A., Yar M., Li T.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
|
2018
|
tom 17
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