Existence and uniqueness of solutions for nonlinear Katugampola fractional differential equations

• Autorzy: Basti Bilal , Arioua Yacine , Benhamidouche Nouredine

Identyfikatory

DOI

10.7862/rf.2019.3

• Języki publikacji: EN

Abstrakty

EN

The present paper deals with the existence and uniqueness of solutions for a boundary value problem of nonlinear fractional differential equations with Katugampola fractional derivative. The main results are proved by means of Guo-Krasnoselskii and Banach fixed point theorems. For applications purposes, some examples are provided to demonstrate the usefulness of our main results.

Słowa kluczowe

EN

fractional equations; fixed point theorems; boundary value problem; existence; uniqueness

PL

równanie ułamkowe; twierdzenie o punkcie stałym; zagadnienie brzegowe; istnienie; wyjątkowość

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2019
• Tom: Vol. 42
• Strony: 35--61
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Basti Bilal

• Laboratory for Pure and Applied Mathematics, University of M’sila, M’sila 28000 ALGERIA

autor

Arioua Yacine

• Laboratory for Pure and Applied Mathematics, University of M’sila, M’sila 28000 ALGERIA

autor

Benhamidouche Nouredine

• Laboratory for Pure and Applied Mathematics, University of M’sila, M’sila 28000 ALGERIA

Bibliografia

• [1] Y. Arioua, N. Benhamidouche, Boundary value problem for Caputo-Hadamard fractional differential equations, Surveys in Mathematics and its Applications 12 (2017) 103–115.
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• [3] K. Diethelm, The Analysis of Fractional Differential Equations, Springer, Berlin, 2010.
• [4] M. El-Shahed, Positive solutions for boundary value problem of nonlinear fractional differential equation, Abstract and Applied Analysis 2007 (2007) 1–8.
• [5] A. Granas, J. Dugundji, Fixed Point Theory, Springer-Verlag, New York, 2003.
• [6] U.N. Katugampola, New approach to a generalized fractional integral, Applied Mathematics and Computation 218 (3) (2011) 860–865.
• [7] U.N. Katugampola, A new approach to generalized fractional derivatives, Mathematical Analysis and Applications 6 (4) (2014) 1–15.
• [8] U.N. Katugampola, Existence and uniqueness results for a class of generalized fractional differential equations, Bull. Math. Anal. Appl., arXiv:1411.5229v1 (2016).
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• [15] K.S. Miller, B. Ross, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York, 1993.
• [16] A.M. Nakhushev, The Sturm–Liouville problem for a second order ordinary differential equation with fractional derivatives in the lower terms, Dokl. Akad. Nauk SSSR 234 (1977) 308–311.
• [17] I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering, Academic Press, New York, 1999.
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Uwagi

PL

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