Constructing reliable approximations of the random fractional Hermite equation: solution, moments and density

Fractional derivatives and integrals (26A33) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Ordinary differential equations and systems with randomness (34F05) Fractional ordinary differential equations (34A08) Random power series in one complex variable (30B20)

Cites Work

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Random Hermite differential equations: mean square power series solutions and statistical properties
The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
Linear fractional differential equations with variable coefficients
Random differential equations in science and engineering
On an operational matrix method based on generalized Bernoulli polynomials of level \(m\)
Fractional-order Riccati differential equation: analytical approximation and numerical results
Extending the deterministic Riemann-Liouville and Caputo operators to the random framework: A mean square approach with applications to solve random fractional differential equations
Applying the random variable transformation method to solve a class of random linear differential equation with discrete delay
Random fractional generalized Airy differential equations: a probabilistic analysis using mean square calculus
On the logistic equation subject to uncertainties in the environmental carrying capacity and initial population density
Modeling biological systems with an improved fractional Gompertz law
A new collection of real world applications of fractional calculus in science and engineering
Solution of a fractional logistic ordinary differential equation
Constructing reliable approximations of the probability density function to the random heat PDE via a finite difference scheme
Analytic-numerical approximating processes of diffusion equation with data uncertainty
Modeling and Inverse Problems in the Presence of Uncertainty
A full probabilistic solution of the random linear fractional differential equation via the random variable transformation technique
Laguerre-type bessel functions