Operational Calculus for Bessel’s Fractional Equation
Purchase on Springer.com
$29.95 / €24.95 / £19.95*
* Final gross prices may vary according to local VAT.
This paper is intended to investigate a fractional differential Bessel’s equation of order 2α with $ \alpha \in]0,1] $ involving the Riemann–Liouville derivative. We seek a possible solution in terms of power series by using operational approach for the Laplace and Mellin transform. A recurrence relation for coefficients is obtained. The existence and uniqueness of solutions is discussed via Banach fixed point theorem.
- J. Butzer, Mellin transform theory and the role of its differential and integral operators. Transform Methods and Special Functions, Varna’96 (Conf. Proc.), Bulgarian Acad. Sci., (1998), 63–83.
- S.D. Eidelman, S.D. Ivasyshen and A.N. Kochubei, Analytic methods in the theory of differential and pseudo-differential equations of parabolic type, Operator Theory: Advances and Applications 152, Birkhäuser, Basel, 2004.
- A.A. Kilbas, M. Rivero, L. Rodríguez-Germá and J.J. Trujillo, Analytic solutions of some linear fractional differential equations with variable coefficients Appl. Math. Comput. 187 (2007), 239–249.
- A. Kilbas, H. Srivastava and J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies 204, Elsevier, Amsterdam, 2006.
- N.N. Lebedev, Special functions and their applications, Translated from Russian by R.A. Silverman, N.J.: Prentice-Hall Inc., Englewood Cliffs, 1965.
- F. Mainardi andM. Tomirotti, Seismic pulse propagation with constant Q and stable probability distributions. Annali di Geofisica 40 (1997), 1311–1328.
- F. Mainardi, Fractional diffusive waves in viscoelastic solids, IUTAM Symposium – Nonlinear Waves in Solids (Conf. Proc.), J.L. Wagnern and F.R. Norwood (editors), (1995), 93–97.
- O.I. Marichev, Handbook of integral transforms of higher transcendental functions: theory and algorithmic tables, translated from Russian by L.W. Longdon, Ellis Horwood Limited, Chichester, 1983.
- I. Podlubny, Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solutions and some applications, Mathematics in Science and Engineering 198, Academic Press, San Diego, 1999.
- A.P. Prudnikov, Yu.A. Brychkov and O.I. Marichev, Integrals and Series, Volume 3: More special functions, translated from Russian by G.G. Gould, Gordon and Breach Publisher, New York, 1990.
- S.G. Samko, A.A. Kilbas, and O.I. Marichev, Fractional integrals and derivatives: theory and applications, Gordon and Breach, New York, 1993, 277–284.
- E.C. Titchmarsh, Introduction to the theory of Fourier integrals, Clarendon Press, Oxford, 1948.
- S. Yakubovich and Y.F. Luchko, The hypergeometric approach to integral transforms and convolutions, Mathematics and Applications 287, Kluwer Academic Publishers, Dordrecht, 1994.
- S. Yakubovich,M.M. Rodrigues and N. Vieira, Fractional two-parameter Schrödinger equation. Preprint CMUP, No. 8, 2011, 12 pp.
- Operational Calculus for Bessel’s Fractional Equation
- Book Title
- Advances in Harmonic Analysis and Operator Theory
- Book Subtitle
- The Stefan Samko Anniversary Volume
- pp 357-370
- Print ISBN
- Online ISBN
- Series Title
- Operator Theory: Advances and Applications
- Series Volume
- Springer Basel
- Copyright Holder
- Springer Basel
- Additional Links
- Fractional differential equations
- Riemann Liouville derivative
- Mellin transform
- Laplace transform
- Bessel equation.
- Industry Sectors
- eBook Packages
- Editor Affiliations
- ID1. , Departamento de Matemática, Universidade de Aveiro
- ID2. , Departamento de Matemática, Universidade de Aveiro
- ID3. Instituto Superior Tecnico, Depto. Matematica, Universidade Tecnica Lisboa
- Author Affiliations
- 1. Center for Research and Development in Mathematics and Applications Department of Mathematics, University of Aveiro Campus Universitário de Santiago, 3810-193, Aveiro, Portugal
- 2. Center of Mathematics of University of Porto Faculty of Science, University of Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal
- 3. Department of Mathematics, Faculty of Science, University of Porto, Rua do Campo Alegre 687, 4169-007, Porto, Portugal
To view the rest of this content please follow the download PDF link above.