An extension of the so-called newit

An extension of the so-called newiterativemethod (NIM) has been used to handle linear and nonlinear fractional partial differential
equations.Themain property of themethod lies in its flexibility and ability to solve nonlinear equations accurately and conveniently.
Therefore, a general framework of the NIM is presented for analytical treatment of fractional partial differential equations in fluid
mechanics. The fractional derivatives are described in the Caputo sense. Numerical illustrations that include the fractional wave
equation, fractional Burgers equation, fractional KdV equation, fractional Klein-Gordon equation, and fractional Boussinesq-like
equation are investigated to show the pertinent features of the technique. Comparison of the results obtained by the NIM with
those obtained by both Adomian decomposition method (ADM) and the variational iteration method (VIM) reveals that the NIM
is very effective and convenient. The basic idea described in this paper is expected to be further employed to solve other similar
linear and nonlinear problems in fractional calculus.

ผลลัพธ์ (แอฟริกา) 1:

'N uitbreiding van die sogenaamde Newiterativemethod (NIM) is gebruik om lineêre en nie-lineêre fraksionele parsiële differensiaal Hanteer
Eiendom van Equations.Themain Themethod lê in sy buigsaamheid en die vermoë om nie-lineêre vergelykings akkuraat en maklik Los.
Dus, 'n algemene raamwerk van die NIM. aangebied is parsiële differensiaalvergelykings vir analitiese behandeling van fraksionele in Fluid
Mechanics. Die fraksionele afgeleide instrumente word beskryf in die Caputo sin. Numeriese illustrasies wat die fraksionele Wave sluit
vergelyking fraksionele Burgers vergelyking fraksionele KHHIW vergelyking fraksionele Klein-Gordon vergelyking en fraksionele Boussinesq-agtige
vergelyking ondersoek na die pertinente eienskappe van die tegniek te toon. Vergelyking van die resultate wat verkry word deur die NIM met resultate
wat verkry word deur beide Adomian ontbinding metode (ADM) en die variety metode iterasie (VIM) toon dat die NIM
is baie effektief en gerieflik. Die basiese idee in hierdie vraestel beskryf word verwag om verder in diens te los Ander soortgelyke
lineêre en nie-lineêre fraksionele Probleme in Calculus.