Existence of Solutions of Fractional Differential Equations via Topological Degree Theory
In this paper, we investigate the existence and uniqueness of solution for a non-linear fractional order differential equation (NFDF) c D
α u ( t ) = f ( t , u ( t ) ) , t ∈ J = [ 0 , 1 ]
u ( o ) = g ( u ) , u ( 1 ) =
δ Γ ( q ) ∫
o T ( t – s )
q – 1 u ( s ) d s
where 1 < α < 2, and 0 < T, s, q ≤ 1, and f: J × R → R is continuous. In this article we use topological degree method for existence os solutions and also for uniqueness of solution
of boundary value NFDE is studied by Banach Constatation principle. At the end we provide an example to demonstrate our main results.
Keywords: Boundary Value Problem; Existence and Uniqueness of Solution; Non Linear Fractional Differential Equations; Topological Degree Method
Document Type: Research Article
Affiliations: Department of Mathematics, University of Malakand, Chakdara, Dir(Lower), Khyber Pakhtunkhwa, 18000, Pakistan
Publication date: 01 January 2016
- Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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