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A quantum system with Razavy type potential which transforms to single or double well potential according to negative or positive potential parameter k, is solved analytically by using extended form of Nikiforov–Uvarov (NU) method. It is presented that eigenvalue spectra of Schrödinger equation for this potential can be attained analytically by the method. Eigenfunction solutions that are depending on confluent Heun polynomials, are analyzed graphically for specified parameters.

In this paper, the graybody radiation phenomena has been handled with the help of fractional calculus. Fractional definition of graybody spectrum has been written in terms of Mittag‐Leffler function. The obtained data from fractional calculus approximation for nearly 2.87 × 107 K have been compared with literature values and standard blackbody radiation.

In this study, we investigate the effect of nonlocality in quantum mechanics and propose a fractional approach the theory of quantized fields. For this purpose, we embedded the fractional calculus to broaden theory of quantum fields since the integral and derivative operators are nonlocal in fractional calculus.Additionally, quantum entanglement is discussed to gain comprehension of nonlocality in the foundation of quantum mechanics. Besides, fractional Lagrangian formalism was presented due to fact that the Lagrangian density is the starting point to establish a field theory.Furthermore, to make fractional field operators quantum mechanical, equal-time commutator have been defined for the these operators in terms of Caputo fractional derivative. Thus, a scheme of quantization of fractional fields is introduced and general aspects of the method is illustrated with the theory of massive scalar fields. This approach laid out to a successful generalization of the quantum field theory which is coherent with the standard formalism. Consequently, we developed promising concept for a quantum field theory by introducing nonlocality into standard mathematical formalism.