Fundamental solutions of the fractional two-parameter telegraph equation

This paper is intended to investigate a fractional telegraph equation of the form with positive real parameters a, b and c. Here , and are operators of the Riemann–Liouville fractional derivative, where 0<α≤1 and 0<β≤1. A symbolic operational form of the solutions in terms of the Mittag–Leffler functions is exhibited. Using the Banach fixed point theorem, the existence and uniqueness of solutions are studied for this kind of fractional differential equations.