Journal
BOUNDARY VALUE PROBLEMS
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1186/s13661-018-1096-6
Keywords
Riemann-Liouville derivative of fractional order; Implicit toppled system; Existence theory; Green function; Ulam stability
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In this manuscript, we give some sufficient conditions for existence, uniqueness and various kinds of Ulam stability for a toppled system of fractional order boundary value problems involving the Riemann-Liouville fractional derivative. Applying the Banach contraction principle and the Leray-Schauder result of cone type, uniqueness and existence results are proved for the proposed toppled system. Stability is investigated by using the classical technique of nonlinear functional analysis. The results obtained are well illustrated with the aid of an example.
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