in this paper, elzaki homotopy perturbation method is employed for solving linear and nonlinear differential equations with a variable coffecient. this method is a combination of elzaki transform and homotopy perturbation method. the aim of using elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as homotopy perturbat...

Abstract The kinetic Brownian motion on the sphere bundle of a Riemannian manifold $$\mathbb {M}$$ M is stochastic process that models random perturbation geodesic flow. If an orientable compact constantly curved surface, we show in limit infinitely large $$L^2$$ L 2</mml:m...

It is often claimed that analysis with infinitesimals requires more substantial use of the Axiom Choice than traditional elementary analysis. The claim based on observation hyperreals entail existence nonprincipal ultrafilters over N, a strong version Choice, while real numbers can be constructed in ZF. axiomatic approach to nonstandard methods refutes this objection. We formulate theory SPOT s...

We solve the Riemann-Hilbert problem on the sphere topology for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincaré accessory parameters. In this way we compute the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infi...

In mathematical modeling, determining most influential parameters on outputs is of major importance. Thus, sensitivity analysis of parameters plays an important role in model validation. We give detailed procedure of constructing a new derivative estimator for general performance measure in Gaussian systems. We will take advantage of using score function and measure-value derivative estimators ...

We solve the Riemann-Hilbert problem on the sphere topology for three singularities of finite strength and a fourth one infinitesimal, by determining perturbatively the Poincaré accessory parameters. In this way we compute the semiclassical four point vertex function with three finite charges and a fourth infinitesimal. Some of the results are extended to the case of n finite charges and m infi...

When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time τ, i.e. the inverse of the decay rate, is the longest characteristic time in the system. However, that need not be true, other times such as the lifetime of an infinitesimal perturbation can be much longer. In the present work, we demonstrate that this ...

We discuss linear perturbations of the most general class teleparallel spacetimes with cosmological symmetry, and perform a decomposition these into irreducible components. then study their behavior under gauge transformations, i.e., infinitesimal diffeomorphisms background spacetime, derive full set gauge-invariant perturbation variables. Comparing our results around diagonal tetrad correspond...

A strong inspiration for studying perturbation theory fractional evolution equations comes from the fact that they have proven to be useful tools in modeling many physical processes. We study of order \(\alpha \in (1,2)\) associated with infinitesimal generator an operator cosine (sine) function generated by bounded time-dependent perturbations a Banach space. show abstract Cauchy problem stron...