Quantum mechanics

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Boundary value problem

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Ordinary differential equation

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Fractional calculus

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Contraction principle

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Boundary Value Problems

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.

Ulam stability to a toppled systems of nonlinear implicit fractional order boundary value problem