1 + 2 t cos ( +)(50)+| x |two tProof. This theorem has been demonstrated earlier [14,46], making use of the formulation with regards to a Mellin arnes integral. Here, we present a proof that arrives straight in the LT of your Mittag effler function. Consider the relation (47). We intend to compute its inverse FT. For starting, let us reverse the roles in the variables t and G (, t) = Apart from, note thatn =(-1)n tn| | n ein two sgn ( n + 1)(51)| | n einand g( x, t) = 1sgn=n ein0 (- ) n e-inR n =(-1)n tn| | n ein 2 sgn ix 1 e d = ( n + 1)1n =(-1)n ein 2 tn ( n + 1) eix d +nn =(-1)n e-in 2 tn ( n + 1) e-ix.