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Hypergeometric foundations of Fokker-Plank like equations
(Elsevier Science, 2016-05)
We discover a deep connection between the Fokker-Planck equation and the hypergeometric differential equation. The same applies to a nonlinear generalization of such equation.
Linear differential equations of fractional order with recurrence relationship
(Natural Sciences Publishing, 2021-01)
This paper introduce the basic general theory for Linear Sequential Fractional Differential Equations which includes a recurrence relationship, involving the Riemann-Liouville fractional operator. The presented equation ...
Hypergeometric connotations of quantum equations
(Elsevier Science, 2016-05)
We show that the Schrödinger and Klein-Gordon equations can both be derived from a hypergeometric differential equation. The same applies to non linear generalizations of these equations.
A family of singular ordinary differential equations of the third order with an integral boundary condition
(Springer, 2018-12)
We establish in this paper the equivalence between a Volterra integral equation of the second kind and a singular ordinary differential equation of the third order with two initial conditions and an integral boundary ...
Combinatorial solutions to the reflection equation
(Academic Press Inc Elsevier Science, 2020-05)
We use ring-theoretic methods and methods from the theory of skew braces to produce set-theoretic solutions to the reflection equation. We also use set-theoretic solutions to construct solutions of the parameter dependent ...
Periodic Orbits and Chaos in Nonsmooth Delay Differential Equations
(World Scientific, 2019-09)
In this paper, we present a method to find periodic solutions for certain types of nonsmooth differential equations or nonsmooth delay differential equations. We apply the method to three examples, the first is a second-order ...
Nonlinear wave equations related to nonextensive thermostatistics
(Molecular Diversity Preservation International, 2017-02)
We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive Sq entropies. Our present contribution is in line with recent developments, where nonlinear ...
On necessary and sufficient conditions for strong hyperbolicity in systems with constraints
(IOP Publishing, 2020-09)
In this work, we study constant-coefficient first order systems of partial differential equations and give necessary and sufficient conditions for those systems to have a well-posed Cauchy problem. In many physical ...
A free boundary problem for a diffusion–convection equation
(Pergamon-Elsevier Science Ltd, 2020-04)
One-dimensional free boundary problem for a nonlinear diffusion - convection equation with a Dirichlet condition at fixed face x=0, variable in time, is considered. Throught several transformations the problem is reduced ...
Sensitivity equations for measure-valued solutions to transport equations
(American Institute of Mathematical Sciences, 2020-01)
We consider the following transport equation in the space of bounded, nonnegative Radon measures M+(Rd): θtμt + θx(v(x)μt) = 0: We study the sensitivity of the solution μt with respect to a perturbation in the vector field, ...