using the riemann-liouville fractional differintegral operator, the lie theory is reformulated. the fractional poisson bracket over the fractional phase space as 3n state vector is defined to be the fractional lie derivative. its properties are outlined and proved. a theorem for the canonicity of the transformation using the exponential operator is proved. the conservation of its generator is p...

this paper deals with the boundary value problem involving the differential equation ell y:=-y''+qy=lambda y, subject to the eigenparameter dependent boundary conditions along with the following discontinuity conditions y(d+0)=a y(d-0), y'(d+0)=ay'(d-0)+b y(d-0). in this problem q(x), d, a , b are real, qin l^2(0,pi), din(0,pi) and lambda is a parameter independent of x. by ...

in this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{t}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. we use a strong convolution technique and derive inclusion results. a radius problem and some other interesting properties of these classes are discussed.

 In this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{T}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

An essential ingredient of the conventional supersymmetric quantum mechanics (for reviews see [1]) is the well known Darboux transformation [2] for the stationary Schrödinger equation. This transformation permits us to construct new exactly solvable stationary potentials from known ones. Similar constructions may be developed for the time-dependent Schrödinger equation [3]. Our approach to Darb...

We introduce the Cauchy augmentation operator for basic hypergeometric series. Heine’s 2φ1 transformation formula and Sears’ 3φ2 transformation formula can be easily obtained by the symmetric property of some parameters in operator identities. The Cauchy operator involves two parameters, and it can be considered as a generalization of the operator T (bDq). Using this operator, we obtain extensi...