Higher-dimensional fractional time-independent Schrodinger equation via fractional derivative with generalised pseudoharmonic potential

In this paper, we obtain approximate bound-state solutions of N-dimensional time-independent fractional Schrodinger equation for the generalised pseudoharmonic potential which has the form V(r alpha)=a1r2 alpha+(a2/r2 alpha)+a3. Here alpha (0<alpha<1) acts like a fractional parameter for the space variable r. The entire study consists of the Jumarie-type fractional derivative and the elegance of Laplace transform. As a result, we can successfully express the approximate bound-state solution in terms of Mittag-Leffler function and fractionally defined confluent hypergeometric function. Our study may be treated as a generalisation of all previous works carried out on this topic when alpha=1 and N arbitrary. We provide numerical result of energy eigenvalues and eigenfunctions for a typical diatomic molecule for different alpha close to unity. Finally, we try to correlate our work with a Cornell potential model which corresponds to alpha=1/2 with a3=0 and predicts the approximate mass spectra of quarkonia.