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RESEARCH PAPER EIGENVALUES FOR ITERATIVE SYSTEMS OF
STURM-LIOUVILLE FRACTIONAL ORDER TWO-POINT
Kapula Rajendra Prasad
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BOUNDARY VALUE PROBLEMS
and Boddu Muralee Bala Krushna
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Abstract
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In this paper, we determine the eigenvalue intervals of λ1 , λ2 , · · ·, λn for which the iterative system of nonlinear Sturm-Liouville fractional order two-point boundary value problem possesses a positive solution by an application of Guo-Krasnosel’skii fixed point theorem on a cone.
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MSC 2010 : Primary 26A33; Secondary 34B15, 34B18 Key Words and Phrases: fractional derivative, boundary value problem, iterative system, two-point, Green’s function, positive solution, eigenvalues 1. Introduction
In recent years, the study of fractional order differential equations has emerged as an important area of mathematics. It has wide range of applications in various fields of science and engineering such as physics, mechanics, control systems, flow in porous media, electromagnetics and viscoelasticity. For some of the recent developments in fractional calculus, we refer to Miller and Ross [19], Samko, Kilbas and Marichev [22], Podlubny [20], Kilbas, Srivasthava and Trujillo [15], Kilbas and Trujillo [16], Diethelm [4], Diethelm and Ford [5], Lakshmikantham and Vatsala [18], Goodrich [7] and the references therein.
c 2014 Diogenes Co., Sofia ° pp. 638–653 , DOI: 10.2478/s13540-014-0190-4
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K.R. Prasad, B.M.B. Krushna
Acknowledgements: The authors thank the referees for their valuable suggestions and comments. References
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EIGENVALUES FOR ITERATIVE SYSTEMS OF . . .
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Department of Applied Mathematics, Andhra University Visakhapatnam, 530 003 – INDIA e-mail:
[email protected] 2
Department of Mathematics, MVGR College of Engineering Vizianagaram, 535 005 – INDIA e-mail:
[email protected] Received: December 15, 2013 Please cite to this paper as published in: Fract. Calc. Appl. Anal., Vol. 17, No 3 (2014), pp. 638–653; DOI: 10.2478/s13540-014-0190-4
