Title :
Exact solutions of simple variational fractional equations on a finite time interval
Author :
Klimek, Malgorzata
Author_Institution :
Inst. of Math. & Comput. Sci., Czestochowa Univ. of Technol., Czestochowa
Abstract :
Simple variational equation containing sum of left-sided and right-sided fractional derivatives is solved. The proposed method includes transformation of the operator of the equation to equivalent Riesz potential and application of composition rules for fractional integrals and derivatives. The general solution is explicitly derived for the homogeneous case and appears to be linear combination of Fox-Wright functions. The conditions of boundedness and continuity for these solutions are studied. Then the nonhomogeneous case is also discussed and solutions in explicit form are derived. As an example the case when order of fractional operators is alpha isin (0, 1) cup (1, 2) is described in detail.
Keywords :
differential equations; Fox-Wright functions; composition rules; equivalent Riesz potential; finite time interval; fractional integrals; left-sided fractional derivatives; nonhomogeneous case; right-sided fractional derivatives; simple variational fractional equations; Biomedical engineering; Calculus; Collaboration; Differential equations; Integral equations; Lagrangian functions; Mathematical model; Physics; Polynomials; Transforms; Euler-Lagrange equations; differential equations; dynamics; fractional differential equations;
Conference_Titel :
Electrotechnical Conference, 2008. MELECON 2008. The 14th IEEE Mediterranean
Conference_Location :
Ajaccio
Print_ISBN :
978-1-4244-1632-5
Electronic_ISBN :
978-1-4244-1633-2
DOI :
10.1109/MELCON.2008.4618419
