Fractional order differential and integral equations with Erdélyi‐Kober operators: Explicit solutions by means of the transmutation method Available to Purchase

By means of the transmutation method we construct explicit solutions of some fractional order Volterra integral equations of second kind, with one or two different Erdélyi‐Kober operators, the latter involving hypergeometric integrals. The same method is applied to fractional differential and differ‐integral equations, involving simultaneously Erdélyi‐Kober fractional integrals and derivatives of different orders. The idea of this method is to use transmutation operators to reduce the solutions of the discussed problems to the known solutions of the simplest problems of the same type (in this case, with Riemann‐Lioville operators). Some illustrative examples are given.