Growth of solutions of a class of linear fractional differential equations with polynomial coefficients

• Autorzy: Hamouda Saada , Mahmoudi Sofiane

Identyfikatory

DOI

10.7494/OpMath.2022.42.3.415

• Języki publikacji: EN

Abstrakty

EN

This paper is devoted to the study of the growth of solutions of certain class of linear fractional differential equations with polynomial coefficients involving the Caputo fractional derivatives by using the generalized Wiman–Valiron theorem in the fractional calculus.

Słowa kluczowe

EN

linear fractional differential equations; growth of solutions; Caputo fractional derivative operator

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2022
• Tom: Vol. 42, no. 3
• Strony: 415--426
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Hamouda Saada

• University Abdelhamid Ibn Badis, Laboratory of Pure and Applied Mathematics, Department of Mathematics and Computer Science, Mostaganem, Algeria

• https://orcid.org/0000-0002-2750-559X

autor

Mahmoudi Sofiane

• University Abdelhamid Ibn Badis, Laboratory of Pure and Applied Mathematics, Department of Mathematics and Computer Science, Mostaganem, Algeria

Bibliografia

• [1] B. Belaidi, K. Hamani, Some results on the complex oscillation theory of differential equations with polynomial coefficients, J. Inequal. Pure Applied Analysis 5 (2004), no. 4, Article 87.
• [2] R.P. Boas, Entire Functions, Academic Press Inc., New York, 1954.
• [3] I. Chyzhykov, N. Semochko, Generalization of the Wiman–Valiron method for fractional dérivatives, Int. J. Appl. Math. 29 (2016), no. 1, 19–30.
• [4] G.G. Gundersen, M. Steinbart, S. Wang, The possible orders of solutions of linear differential equations with polynomial coefficients, Trans. Amer. Math. Soc. 350 (1998), 1225–1247.
• [5] W.K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
• [6] G. Jank, L. Volkmann, Einfuhrung in die Theorie der ganzen und meromorphen Funktionen mit Anwendungen auf Differentialgleichungen, Birkhäuser, Basel-Boston-Stuttgart, 1985.
• [7] A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006.
• [8] I. Laine, Nevanlinna Theory and Complex Differential Equations, W. de Gruyter, Berlin, 1993.
• [9] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
• [10] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
• [11] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York, 1993.
• [12] G. Valiron, Lectures on the General Theory of Integral Functions, translated by E.F. Collingwood, Chelsea, New York, 1949.
• [13] H. Wittich, Neuere Untersuchungen uber eindeutige analytische Funktionen, 2nd ed., Springer-Verlag, Berlin–Heidelberg–New York, 1968.
• [14] L. Yang, Value Distribution Theory, Springer-Verlag Science Press, Berlin–Beijing, 1993.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).