The analytical solution of Van der Pol and Lienard differential equations within conformable fractional operator by retarded integral inequalities

• Autorzy: Usta Fuat , Sarıkaya Mehmet Zeki

Identyfikatory

DOI

10.1515/dema-2019-0017

• Języki publikacji: EN

Abstrakty

EN

In this study we introduced and tested retarded conformable fractional integral inequalities utilizing non-integer order derivatives and integrals. In line with this purpose, we used the Katugampola type conformable fractional calculus which has several practical properties. These inequalities generalize some famous integral inequalities which provide explicit bounds on unknown functions. The results provided here had been implemented to the global existence of solutions to the conformable fractional differential equations with time delay.

Słowa kluczowe

EN

global existence; retarded integral inequalities; conformable fractional Van der Pol differential equation; conformable fractional Liènard differential equation

PL

nierówności całkowe; równanie różniczkowe; pochodna ułamkowa

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 204--212
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Usta Fuat

• Düzce University, Turkey

autor

Sarıkaya Mehmet Zeki

• Düzce University, Turkey

Bibliografia

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• [6] Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, 1993
• [7] Abdeljawad T., On conformable fractional calculus, J. Comput. Appl. Math., 2015, 279, 57-66
• [8] Qayyum A., Faye I., Shoaib M., On new generalized inequalities via Riemann-Liouville fractional integration, J. Fract. Calc. Appl., 2015, 6(1), 91-100
• [9] Yavuz M., Novel solution methods for initial boundary value problems of fractional order with conformable differentiation, An International Journal of Optimization and Control: Theories & Applications, 2018, 8(1), 1-7
• [10] Yavuz M., Özdemir N., New numerical techniques for solving fractional partial differential equations in conformable sense, In: Ostalczyk P., Sankowski D., Nowakowski J. (Eds.), Non-integer Order Calculus and its Applications, Lecture Notes in Electrical Engineering, vol. 496, Springer, Cham, 2019, 49-62
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• [12] Yavuz M., Özdemir N., On the solutions of fractional Cauchy problem featuring conformable derivative, Proceedings, ITM Web of Conferences, EDP Sciences, 2018, 22, 01045
• [13] Katugampola U., A new fractional derivative with classical properties, ArXiv:1410.6535v2

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).