Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Powiadomienia systemowe

Sesja wygasła!

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Meijer G-functions series as exact solutions of a class of non-homogeneous fractional differential equations

Klimek M., Dziembowski D.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2009

Vol. 8, nr 2

71-85

A fractional differential equation of real order α, containing variable coefficient t β and a non-homogeneous term, is solved. The general solution is obtained as a sum of Meijer G-functions series determining the solution of a homogeneous counterpart of the considered equation and a series representing the particular solution of a non-homogeneous equation. The convergence of the respective series is analyzed in detail using theorems on properties of Meijer G functions. As an example, two equations, with β = 0 and β = α /2 are studied.

On Mellin transform application to solution of fractional differential equations

Klimek M., Dziembowski D.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2008

Vol. 7, nr 2

31-41

The Mellin transform method is applied to fractional differential equations with a right-sided derivative and variable potential. After solving the intermediate difference equation we arrive at the general solution of the problem in the form of a Meijer-G-function series. Using the symmetry properties of fractional derivatives we transform it into a general solution for an analogous equation with the left-sided Riemann-Liouville derivative. Two examples are studied in detail and an explicit form of component solutions is given.