Analytic charged BHs in f(R) gravity

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