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In this paper, we extend the basic model of the restricted four-body problemintroducing two bigger dominant primaries $m_1$ and $m_2$ as oblate spheroidswhen masses of the two primary bodies ($m_2$ and $m_3$) are equal. The aim ofthis study is to investigate the use of zero velocity surfaces and thePoincar\'{e} surfaces of section to determine the possible allowed boundaryregions and the stability orbit of the equilibrium points. According todifferent values of Jacobi constant $C$, we can determine boundary region wherethe particle can move in possible permitted zones. The stability regions of theequilibrium points expanded due to presence of oblateness coefficient andvarious values of $C$, whereas for certain range of $t$ ($100 \le t \le 200$),orbits form a shape of cote's spiral. For different values of oblatenessparameters $A_1~ (0<A_1<1)$ and $A_2~ (0<A_2<1)$, we obtain two collinear andsix non-collinear equilibrium points. The non-collinear equilibrium points arestable when the mass parameter $\mu$ lies in the interval($0.0190637,~0.647603$). However, basins of attraction are constructed with thehelp of Newton Raphson method to demonstrate the convergence as well asdivergence region of the equilibrium points. The nature of basins of attractionof the equilibrium points are less effected in presence and absence ofoblateness coefficients $A_1$ and $A_2$ respectively in the proposed model.

Stability Regions of Equilibrium Points in Restricted Four-Body Problem with Oblateness Effects