In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.

In this paper, the estimation of a scale parameter t under a new and bounded loss function, based on a reflection of the gamma density function, is discussed. The best scale-invariant estimator of tis obtained and the admissibility of all linear functions of the sufficient statistic, for estimating t in the absence of a nuisance parameter, is investigated

Whereas the analysis of loops in imperative programs is, justifiably, dominated by the concept of invariant assertion, we submit a related but different concept, of invariant relation, and show how it can be used to compute or approximate the function of a while loop. We also introduce the concept of invariant function, which is used to generate a broad class of invariant relations.

Let W (ψ; x, y) be the wideband ambiguity function. It is obtained in this note that y− α+2 2 W (ψ;x, y)(α > −1) is SO(2)-invariant if and only if the Fourier transform of ψ is a Laguerre function.

We prove that the existence of a homogeneous invariant of degree n for a representation of a semi-simple Lie group guarantees the existence of non-trivial solutions of D α = 0: these correspond to the maximum value of the square of the invariant divided by the norm of the representation to the n th power.

Our principal interest in this paper is to study higher order degenerate Hermite-Bernoulli polynomials arising from multivariate $p$-adic invariant integrals on $mathbb{Z}_p$. We give interesting identities and properties of these polynomials that are derived using the generating functions and $p$-adic integral equations. Several familiar and new results are shown to follow as special cases. So...

In this paper, at first the elemantary and basic concepts of multiplicative discrete and continous differentian and integration introduced. Then for these kinds of differentiation invariant functions the general solution of discrete and continous multiplicative differential equations will be given. Finaly a vast class of difference equations with variable coefficients and nonlinear difference e...