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Mean square calculus and random linear fractional differential equations: Theory and applications

C. Burgos

C. Burgos

Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de ValenciaValencia, Spain
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Burgos, C.
, 
J.C Cortés

J.C Cortés

Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de ValenciaValencia, Spain
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Cortés, J.C
, 
L. Villafuerte

L. Villafuerte

Department of Mathematics, University of Texas at AustinAustin, USA
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Villafuerte, L.
 et 
R.J. Villanueva

R.J. Villanueva

Instituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de ValenciaValencia, Spain
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Villanueva, R.J.
  
28 juil. 2017
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Publié en ligne: 28 juil. 2017
Pages: 317 - 328
Reçu: 04 avr. 2017
Accepté: 28 juil. 2017
DOI: https://doi.org/10.21042/AMNS.2017.2.00026
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© 2017 C. Burgos, J.C Cortés, L. Villafuerte, R.J. Villanueva, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Figure 1

Approximations of the mean (left) and the standard deviation (rigth) of the solution SP to the random IVP (2)α = 0.7 and λ = 3/4 using different orders of truncations M = 6, 7, 8, 9, 10 over the time interval [0, 5].
Approximations of the mean (left) and the standard deviation (rigth) of the solution SP to the random IVP (2)α = 0.7 and λ = 3/4 using different orders of truncations M = 6, 7, 8, 9, 10 over the time interval [0, 5].

Figure 2

Approximations of the mean (left) and the standard deviation (right) of the solution SP to the random IVP (2) with α = 0.7 and λ = 5/4 using different orders of truncations M = 10, 12, 14, 16, 18 over the time interval [0,5].
Approximations of the mean (left) and the standard deviation (right) of the solution SP to the random IVP (2) with α = 0.7 and λ = 5/4 using different orders of truncations M = 10, 12, 14, 16, 18 over the time interval [0,5].

Figure 3

Approximations of the mean (left) and the standard deviation (right) of the solution SP to the random IVP (2) with α = 0.7, λ = 5/4, E[b0]=E[c]=−1 $\mathbb{E}[b_0]=\mathbb{E}[c]=-1$ and V[b0]=V[c]=1/4 $\mathbb{V}[b_0]=\mathbb{V}[c]=1/4$ using different orders of truncations M over the time intervals [0,5].
Approximations of the mean (left) and the standard deviation (right) of the solution SP to the random IVP (2) with α = 0.7, λ = 5/4, E[b0]=E[c]=−1 $\mathbb{E}[b_0]=\mathbb{E}[c]=-1$ and V[b0]=V[c]=1/4 $\mathbb{V}[b_0]=\mathbb{V}[c]=1/4$ using different orders of truncations M over the time intervals [0,5].

Figure 4

Approximations of the mean (left) and the standard deviation (right) of the solution SP to the random IVP (2) with M = 20, λ = 5/4, E[b0]=E[c]=−1 $\mathbb{E}[b_0]=\mathbb{E}[c]=-1$ and V[b0]=V[c]=1/4 $\mathbb{V}[b_0]=\mathbb{V}[c]=1/4$ using different orders of the derivative α = {0.4, 0.5, 0.6, 0.7, 0.99} over the time interval [0, 5].
Approximations of the mean (left) and the standard deviation (right) of the solution SP to the random IVP (2) with M = 20, λ = 5/4, E[b0]=E[c]=−1 $\mathbb{E}[b_0]=\mathbb{E}[c]=-1$ and V[b0]=V[c]=1/4 $\mathbb{V}[b_0]=\mathbb{V}[c]=1/4$ using different orders of the derivative α = {0.4, 0.5, 0.6, 0.7, 0.99} over the time interval [0, 5].
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