In this work, we study the formal connections between non-linear Fokker-Planck Equation associated with non-additive entropy and Boltzmann correlation functional. The collisional term following $q$-algebra is adopted. derivation of Equation, two constraints are imposed on final result: i) that entropic index $q$ a characteristic parameter systems value does not change time, ii) for $q \rightarr...

in this present work, the kudryashov method and the functional variable method are used to construct exact solutions of the complex kdv equation. the kudryashov method and the functional variable method are powerful methods for obtaining exact solutions of nonlinear evolution equations.

We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients our operator depend polynomially space variables, while noise is additive, white time and coloured space. provide sufficient condition spectral measure covariance functional describing that allows for existence random field solution ...

In the present paper a solution of the generalizedquadratic functional equation$$f(kx+ y)+f(kx+sigma(y))=2k^{2}f(x)+2f(y),phantom{+} x,yin{E}$$ isgiven where $sigma$ is an involution of the normed space $E$ and$k$ is a fixed positive integer. Furthermore we investigate theHyers-Ulam-Rassias stability of the functional equation. TheHyers-Ulam stability on unbounded domains is also studied.Applic...

In this article, we introduce a class of the generalized mixed additive, quadratic and quartic functional equations and obtain their common solutions. We also investigate the stability of such modified functional equations in the non-Archimedean normed spaces by a fixed point method.

For the quantum integer [n]q = 1+q+q + · · ·+q there is a natural polynomial multiplication such that [mn]q = [m]q ⊗q [n]q . This multiplication is described by the functional equation fmn(q) = fm(q)fn(q ), defined on a given sequence F = {fn(q)} ∞ n=1 of polynomials such that fn(0) = 1 for all n. If F = {fn(q)} ∞ n=1 is a solution of the functional equation, then there exists a formal power se...

In this article, we defined the generalized intuitionistic P-pseudo fuzzy 2-normed spaces and investigated Hyers stability of m-mappings in space. The are interesting functional equations; these equations additive for m = 1, quadratic 2, cubic 3, quartic 4. We have four types by fixed point method.