In this article, we seek exact charged spherically symmetric black holes (BHs) with considering $f(R)$ gravitational theory. This BH is characterized by convolution and error functions. Those two functions depend on a constant of integration which is responsible to make such a solution deviate from Einstein's general relativity (GR). The error function which constitutes the charge potential of the Maxwell field depends on the constant of integration and when this constant is vanishing we can not reproduce Reissner-Nordström BH in the lower order of $f(R)$. This means that we can not reproduce Reissner-Nordström BH in lower-order–curvature theory, i.e., in GR limit $f(R)=R$, we can not get the well known charged BH. We study the physical properties of these BHs and show that it is asymptotically approached as a flat spacetime or approach AdS/dS spacetime. Also, we calculate the invariants of the BHS and show that the singularities are milder than those of BH's of GR. Additionally, we derive the stability condition through the use of geodesic deviation. Moreover, we study the thermodynamics of our BH and show the effect of the higher-order–curvature theory. Finally, we study the stability analysis using the odd-type mode and show that all the BHs are stable and have radial speed equal to one.

在本文中，我们寻求精确的带电球对称黑洞 (BH)，并考虑 $F(\mathrm{电阻})$引力理论。这个 BH 的特点是卷积和误差函数。这两个函数取决于积分常数，积分常数负责使这样的解偏离爱因斯坦的广义相对论 (GR)。构成麦克斯韦场电荷电势的误差函数取决于积分常数，当该常数消失时，我们无法以低阶重现 Reissner-Nordström BH$F(\mathrm{电阻})$. 这意味着我们不能在低阶曲率理论中重现 Reissner-Nordström BH，即在 GR 极限中$F(\mathrm{电阻})=\mathrm{电阻}$，我们不能得到众所周知的带电BH。我们研究了这些 BH 的物理特性，并表明它是作为平坦时空渐近接近的或接近 AdS/dS 时空的。此外，我们计算了 BHS 的不变量并表明奇点比 GR 的 BH 的奇点温和。此外，我们通过使用测地线偏差推导出稳定性条件。此外，我们研究了 BH 的热力学并展示了高阶曲率理论的影响。最后，我们研究了使用奇型模式的稳定性分析，表明所有 BH 都是稳定的，径向速度等于 1。