Fractional Equations and Models by Trifce Sandev & Živorad Tomovski

Author:Trifce Sandev & Živorad Tomovski
Language: eng
Format: epub
ISBN: 9783030296148
Publisher: Springer International Publishing

(4.284)

where , . The inverse Laplace transform of (4.284) yields

(4.285)

Finally, by inverse Fourier transform of relation (4.285) we finish the proof of the theorem.

Example 4.9 ([110])

The solution of the fractional diffusion equation (4.280) with boundary conditions (4.281) and initial condition g(x) = δ(x) is given by

(4.286)

where is the Fox’ H-function (1.​40).

Indeed, by using , the cosine transform (1.​50) and the properties of H-function, we obtain

(4.287)

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