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Existence of Solutions of Three-Dimensional Fractional Differential Systems
Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affli. to Periyar University), Rasipuram, India
Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affli. to Periyar University), Rasipuram, India
Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affli. to Periyar University), Rasipuram, India
- 1 Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affli. to Periyar University), Rasipuram, India
- 2 Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affli. to Periyar University), Rasipuram, India
- 3 Post Graduate and Research Department of Mathematics, Thiruvalluvar Government Arts College (Affli. to Periyar University), Rasipuram, India
Applied Mathematics·Volume 08 (2017)·Pages 193–208·Published 7 February 2017·DOI10.4236/am.2017.82016
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Abstract
In this article, we consider the three-dimensional fractional differential system of the form together with the Neumann boundary conditions, where are the standard Caputo fractional derivatives, . A new result on the existence of solutions for a class of fractional differential system is obtained by using Mawhin’s coincidence degree theory. Suitable examples are given to illustrate the main results.
KeywordsFractional Differential EquationsBoundary Value ProblemCoincidence Degree Theory
- Miller, K.S. and Ross, B. (1993) An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York.
- Samko, S.G., Kilbas, A.A. and Marichev, O.I. (1993) Fractional Integrals and Derivatives. Gordon and Breach Science Publishers, Yverdon.
- Hilfer, Z. (2000) Appliations of Fractional Calculus in Physics. World Scientific, Singapore. https://doi.org/10.1142/3779
- Metzler, R. and Klafter, J. (2000) Boundary Value Problems for Fractional Diffusion Equations. Physics A, 278, 107-125. https://doi.org/10.1016/S0378-4371(99)00503-8
- Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006) Theory and Applications of Fractional Differential Equations. Elsevier, Amsterdam.
- Lakshmikantham, V., Leela, S. and Vasundhara Devi, J. (2009) Theory of Fractional Dynamic Systems. Cambridge Academic Publishers, Cambridge.
- Mainardi, A. (2010) Fractional Calculus and Waves in Linear Viscoelasticity. Imperial College Press, London. https://doi.org/10.1142/p614
- Abbas, S., Benchora, M. and N’Guerekata, G.M. (2012) Topics in Fractional Differential Equations. Springer, New York. https://doi.org/10.1007/978-1-4614-4036-9
- Zhou, Y. (2014) Basic Theory of Fractional Differential Equations. World Scientific, Singapore. https://doi.org/10.1142/9069
- Ahmad, B. and Nieto, J.J. (2009) Existence Results for a Coupled System of Nonlinear Fractional Differential Equations with Three-Point Boundary Conditions. Computers and Mathematics with Applications, 58, 1838-1843. https://doi.org/10.1016/j.camwa.2009.07.091
- Liu, Y., Ahmad, B. and Agarwal, R.P. (2013) Existence of Solutions for a Coupled System of Nonlinear Fractional Differential Equations with Fractional Boundary Conditions on the Half-Line. Advances in Difference Equations, 2013, 46. https://doi.org/10.1186/1687-1847-2013-46
- Aphithana, A., Ntouyas, S.K. and Tariboon, J. (2015) Existence and Uniqueness of Symmetric Solutions for Fractional Differential Equations with Multi-Point Fractional Integral Conditions. Boundary Value Problems, 2015, 68. https://doi.org/10.1186/s13661-015-0329-1
- Wang, Y. (2016) Positive Solutions for Fractional Differential Equation Involving the Riemann-Stieltjes Integral Conditions with Two Parameters. Journal of Nonlinear Science and Applications, 9, 5733-5740.
- Mawhin, J. (1993) Topological Degree and Boundary Value Problems for Nonlinear Differential Equations in Topological Methods for Ordinary Differential Equations. Lecture Notes in Mathematics, 1537, 74-142. https://doi.org/10.1007/BFb0085076