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We show that from an appropriate manipulation of the biconfluent Heun differential equation can obtain the correct expression for the energy eigenvalues for the Klein-Gordon equation without potential in the background of Som-Raychaudhuri space-time with a cosmic string as a case particular (k L = 0) of [Vitória et al. Eur. Phys. J. C (2018) 78:44], in opposition what was stated in a recent paper published in this journal [F. Ahmed, Eur. Phys. J. C (2019) 79:682].

The relativistic quantum motion of scalar bosons under the influence of a full vector (minimal A µ and nonminimal X µ ) and scalar (V s ) interactions embedded in the background of a cosmic string is explored in the context of the Klein-Gordon equation. Considering Coulomb interactions, the effects of this topological defect in equation of motion, phase shift and S-matrix are analyzed and discussed. Bound-state solutions are obtained from poles of the S-matrix and it is shown that bound-state solutions are possible only for a restrict range of coupling constants. PACS. 0 4.62.+v -0 4.20.Jb -0 3.65.Ge -0 3.65.Pm

We point out a misleading treatment in a recent paper published in this Journal (Sobhani et al., Eur Phys J C 78:106, 2018) regarding solutions for the Schrödinger equation with a anharmonic oscillator potential embedded in the background of a cosmic string mapped into biconfluent Heun equation. This fact jeopardizes the thermodynamical properties calculated in this system.In a recent paper in this Journal, Sobhami et. al. [1] have studied the thermodynamical properties of the anharmonic oscillator within cosmic-string framework using ordinary statistic and the q-deformed superstatistics approaches. To achieve their goal, the authors need to calculate the wave function and the energy spectrum, which have been obtained from the Schrödinger equation within a cosmic-string framework mapped into biconfluent Heun differential equation. It is worthwhile to mention that all results depend mainly on the energy spectrum of the system. The purpose of this comment is point to out a misleading treatment on the solution of the biconfluent Heun equation, this fact jeopardizes the results of [1].The time-independent Schrödinger equation with an anharmonic oscillator potential embedded in the background of a cosmic string is given byRedefining the wave function as Φ(ρ) = R(ρ) √ ρ , one can remove the first derivative and rewrite Eq.(1) as a

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