Fractional problems with right-handed Riemann-Lioville fractional derivatives

• Autorzy: Jankowski T.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems are also discussed. A few examples illustrate the results

Słowa kluczowe

EN

right-handed Riemann-Liouville fractional derivatives; nonlinear boundary problems; linear problems; existence of solutions; Mittag-Leffler functions

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2016
• Tom: Vol. 20, No 1
• Strony: 63--83
• Opis fizyczny: Bibliogr. 21 poz.

Twórcy

autor

Jankowski T.

• Department of Differential Equations and Applied Mathematics Gdansk University of Technology Narutowicza 11/12, 80-233 Gdansk, Poland

Bibliografia

• [1] Kilbas A A, Srivastava R H and Trujillo J J 2006 Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Elsevier, 204
• [2] Al-Bassam M A 1965 J. Reine Angew. Math. 218 70
• [3] Jankowski T 2008 Dynam. Systems Appl. 17 677
• [4] Jankowski T 2013 Appl. Math. Lett. 26 344
• [5] Jankowski T 2013 Appl. Math. Comput. 219 7772
• [6] Jankowski T 2013 Appl. Math. Comput. 219 9155
• [7] Kilbas A A, Bonilla B and Trukhillo Kh 2000 Dokl. Nats. Akad. Nauk Belarusi 44 18 (Russian)
• [8] Kilbas A A and Marzan A S 2003 Dokl. Nats. Akad. Nauk Belarusi 47 29 (Russian)
• [9] Lakshmikantham V, Leela S and Vasundhara J 2009 Theory of Fractional Dynamic Systems, Cambridge Academic Publishers
• [10] Lin L, Liu X and Fang H 2012 Elektron. J. Differential Equations 100 1
• [11] Liu Z, Wang R 2013 Abstr. Appl. Anal., Art. ID 432941
• [12] Liu Z, Sun J, Sz´ant´o I 2013 Results Math 63 1277
• [13] McRae A F 2009 Nonlinear Anal. 71 6093
• [14] Ramirez D J and Vatsala S A 2009 Opuscula Math. 29 289
• [15] Samko G S, Kilbas A A and Marichev I O 1993 Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers
• [16] Wang G 2012 J. Comput. Appl. Math. 236 2425
• [17] Wang G, Liu S, Baleanu D and Zhang L 2013 Adv. Difference Equ. 2013:280
• [18] Wei Z, Li G and Che J 2010 J. Math. Anal. Appl. 367 260
• [19] Zhang S 2009 Nonlinear Anal. 71 2087
• [20] Zhang S and Su X 2011 Comput. Math. Appl. 62 1269
• [21] Jankowski T 2014 Appl. Math. Lett. 28 14

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę