Time fractional equations and probabilistic representation
نویسندگان
چکیده
منابع مشابه
TIME - FRACTIONAL EQUATIONS Marko Kostić
The fractional calculus is one of the active research fields in mathematical analysis, primarily from its importance in modeling of various problems in engineering, physics, chemistry and other sciences. Presumably the first systematic exposition on abstract time-fractional equations with Caputo fractional derivatives is that of Bazhlekova [2]. In this fundamental work, the abstract time-fracti...
متن کاملSolving nonlinear space-time fractional differential equations via ansatz method
In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...
متن کاملOn time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کاملApplications of He’s Variational Principle method and the Kudryashov method to nonlinear time-fractional differential equations
In this paper, we establish exact solutions for the time-fractional Klein-Gordon equation, and the time-fractional Hirota-Satsuma coupled KdV system. The He’s semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply He’s semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the time-fractiona...
متن کاملFractional representation formulae and right fractional inequalities
Here we prove fractional representation formulae involving generalized fractional derivatives, Caputo fractional derivatives and Riemann–Liouville fractional derivatives. Then we establish Poincaré, Sobolev, Hilbert–Pachpatte and Opial type fractional inequalities, involving the right versions of the abovementioned fractional derivatives.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos, Solitons & Fractals
سال: 2017
ISSN: 0960-0779
DOI: 10.1016/j.chaos.2017.04.029