Random differential equations as models of ecosystems— III. bayesian inference for parameters

Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.

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On nth-order nonlinear ordinary random differential equations

Nonlinear Oscillations ◽

10.1007/s11072-011-0129-1 ◽

2011 ◽

Vol 13 (4) ◽

pp. 535-549 ◽

Cited By ~ 2

Author(s):

B. C. Dhage

Keyword(s):

Differential Equations ◽

Random Differential Equations

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A deep learning solution approach for high-dimensional random differential equations

Probabilistic Engineering Mechanics ◽

10.1016/j.probengmech.2019.05.001 ◽

2019 ◽

Vol 57 ◽

pp. 14-25 ◽

Cited By ~ 7

Author(s):

Mohammad Amin Nabian ◽

Hadi Meidani

Keyword(s):

Deep Learning ◽

Differential Equations ◽

High Dimensional ◽

Solution Approach ◽

Random Differential Equations

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Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽

10.3390/sym11020143 ◽

2019 ◽

Vol 11 (2) ◽

pp. 143

Author(s):

Chayut Kongban ◽

Poom Kumam ◽

Juan Martínez-Moreno ◽

Kanokwan Sitthithakerngkiet

Keyword(s):

Differential Equation ◽

Fixed Point ◽

Differential Equations ◽

Stochastic Differential Equation ◽

Fixed Point Theorems ◽

Metric Spaces ◽

Random Fixed Point ◽

Contractive Mappings ◽

Random Differential Equations ◽

Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

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