Linear algebraic foundations of the operational calculi

Operational calculus for the solution of fractional differential equations with noncommensurate orders

“…In previous works, 15,17 a general algebraic operational calculus suitable for solving commensurate order linear equations was introduced. Here, we will generalize that framework in order to deal with the case of noncommensurate orders.…”

“…3. Similarly, we join the pseudo-pole −3 of order 0.5 to pre-existing solution (15), obtaining (t) = 0.5 E −3,0 (t) * 0.3 E −2,0 (t) * ( −1,0 (t) + 2 0,−1 (t) + 7 0,0 (t)…”

“…Here, we use a different approach on the basis of a general operational calculus. 15 We propose an algebraic version of the usual convolution product. From it, we construct several algebraic rules, [16][17][18] which lead to a new approach for dealing with linear time invariant systems.…”