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.

the euler-lagrange equation plays an important role in the minimization problems of the calculus of variations. this paper employs the differential transformation method (dtm) for finding the solution of the euler-lagrange equation which arise from problems of calculus of variations. dtm provides an analytical solution in the form of an infinite power series with easily computable components. s...

A. In this paper, our aim is to incorporateGauss’s famous law in electrodynamics and some of Cauchy’s results in residue calculus within the general setting of deRham cohomology, that will be shown to provide amost natural environment for their development. Namely, it will be demonstrated that forms defined and closed on punctured spaces can be assigned a residue similar to the one defin...

A numerical algorithm based upon the residue calculus for computing the three-dimensional anisotropic elastic Green’s function and its derivatives has been presented by, among the others, Sales and Gray. Although this residue approach is in general faster than the standard Wilson–Cruse interpolation scheme, the convergence rate and accuracy can seriously degrade in the neighborhood of a non-sim...

The Euler-Lagrange equation plays an important role in the minimization problems of the calculus of variations. This paper employs the differential transformation method (DTM) for finding the solution of the Euler-Lagrange equation which arise from problems of calculus of variations. DTM provides an analytical solution in the form of an infinite power series with easily computable components. S...

We present an exposition of the basic properties of the Jacobi symbol, with a method of calculating it due to Eisenstein. Fix a prime p. For an integer a relatively prime to p the Legendre symbol is defined by (a/p) = 1 if a is a quadratic residue (mod p) and (a/p) =−1 if a is a quadratic nonresidue (mod p). We recall Euler’s theorem that (a/p) ≡ a(p−1)/2 (mod p). We have the famous Law of Quad...

We give new a proof of the general Briançon-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a related result for the ideal generated by the the subdeterminants of a matrix-valued generically surjective holomorphic function, generalizing the duality theorem fo...

Gravitational lensing has proven to be not only important astrophysically, but intriguing mathematically as well. Mathematical investigations of gravitational lens theory have yielded important results and insights, employing techniques and results from such disparate areas as catastrophe theory, differential geometry and Morse theory. In this paper, we illustrate how another seemingly unrelate...

In this paper I extend the standard first-order resolution method with special reasoning mechanisms for sorts. Sorts are unary predicates. Literals built from unary predicates are called sort literals. Negative sort literals can be compiled into restrictions of the relevant variables to sorts or can be deleted if they fulfill special conditions. Positive sort literals define the sort-theory. So...