ON SOLVABILITY OF THE THIRD PSEUDO-PARABOLIC FRACTIONAL EQUATION WITH PURELY NONLOCAL CONDITIONS
The aims of this paper are to present a numerical technique for solving the one-dimensional pseudo-parabolic fractional differential equation that combines classical and integral conditions:
where for any positive integer the gamma function Γ and the left Caputo derivative are respectively, defined as
(i)
(ii)
A Laplace transform technique is introduced for solving the considered equation approximating the definite integrals by high-precision quadrature schemes. To invert the equation numerically back into the time domain, we apply the Stehfest inversion algorithm.
Caputo fractional derivative, Laplace transform method, pseudo-parabolic fractional equation, Stehfest inversion algorithm, energy-integral.