A succinct presentation of the algebraic structure of the quantized Klein-Gordon field can be given in terms of a Lorentz invariant inner product. A presentation of a classical Klein-Gordon random field at non-zero temperature can be given in the same noncommutative algebraic style, allowing a detailed comparison of the quantized Klein-Gordon field with a classical Klein-Gordon random field.

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

304 3.5. Namboodiri. kl. A. A,. Nakai. C‘. k Klein, 1). C. (1070) J. Ncurochem. 33. 807-810 30. Klein. 1). C’. k Namboodiri, M. A. A. (1082) Trends Biochem. Sci. 7, OXI02 37. Namboodiri, M. A. A,, Weller, J. I , . Kc Klein, I). C’. (1080) J. l k l . Cheni. 255. 6032-0035 38. Namboodiri, M. A. A,. Weller, J. I, . K: Klein, I). C’. ( 1080) Hiochem. Hiophys. Kes. C’ommun. 96, 1 8%1 05 30 . Niimboo...

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

‎ in this paper, we investigate stability analysis of fractional differential systems equipped with the conformable fractional derivatives. some stability conditions of fractional differential systems are proposed by applying the fractional exponential function and the fractional laplace transform. moreover, we check the stability of conformable fractional lotka-volterra system with the multi-st...

‎It is commonly accepted that fractional differential equations play‎ ‎an important role in the explanation of many physical phenomena‎. ‎For‎ ‎this reason we need a reliable and efficient technique for the‎ ‎solution of fractional differential equations‎. ‎This paper deals with‎ ‎the numerical solution of a class of fractional differential‎ ‎equation‎. ‎The fractional derivatives are described...

We show asymptotic completeness for the charged Klein–Gordon equation in exterior De Sitter–Reissner–Nordström spacetime when product of charge black with Klein-Gordon field is small enough. then interpret scattering as transports along principal null geodesics a Kaluza–Klein extension original spacetime.

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...