The fourth-order ordinary differential equation with the fractional initial/boundary conditions

• Autorzy: Siedlecki Jarosław

Identyfikatory

DOI

10.17512/jamcm.2020.1.07

• Języki publikacji: EN

Abstrakty

EN

The initial/boundary value problem for the fourth-order homogeneous ordinary differential equation with constant coefficients is considered. In this paper, the particular solutions an ordinary differential equation with respect to the set of boundary conditions are studied. At least one of the boundary conditions is described by a fractional derivative. Finally, a few illustrative examples of particular solutions to the considered problem are shown.

Słowa kluczowe

EN

fractional calculus; ordinary differential equation; analytical solution

PL

rachunek ułamkowy; równanie różniczkowe zwyczajne; rozwiązanie analityczne; warunek brzegowy

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2020
• Tom: Vol. 19, nr 1
• Strony: 79--87
• Opis fizyczny: Bibliogr. 9 poz., rys.

Twórcy

autor

Siedlecki Jarosław

• Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland

Bibliografia

• [1] Abell, M.L., & Braselton, J.P. (2014). Introductory Differential Equations with Boundary Value Problems. 4th Ed., Academic Press, Elsevier Inc.
• [2] Boyce, W.E., DiPrima, R.C., & Meade, D.B. (2017). Elementary Differential Equations and Boundary Value Problems. 11th Ed., John Wiley & Sons, Inc.
• [3] Agarwal, R.P. (1986). Boundary Value Problems for Higher Order Differential Equations. Singapore, Philadelphia: World Scientific.
• [4] Polyanin, A.D., & Zaitsev, V.F. (2017). Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems. 3rd Ed., Chapman and Hall/CRC.
• [5] Aftabizadeh, A.R. (1986). Existence and uniqueness theorems for fourth order boundary value problems. J. Math. Anal. Appl., 116, 415-426.
• [6] Kilbas, A.A., Srivastava, H.M., & Trujillo, J.J. (2006). Theory and Applications of Fractional Differentia Equations. Amsterdam: Elsevier.
• [7] Podlubny, I. (1999). Fractional differential equations: an introduction to fractional derivatives,fractional differential equations, to methods of their solution and some of their applications (Vol. 198). Elsevier.
• [8] Kukla, S., & Siedlecka, U. (2016). Fractional heat conduction in multilayer spherical bodies. Journal of Applied Mathematics and Computational Mechanics, 15(4), 83-92.
• [9] Ciesielski, M., & Blaszczyk, T. (2018). An exact solution of the second order differential equation with the fractional/generalised boundary conditions. Advances in Mathematical Physics, Article ID 7283518.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).