The uniqueness of a solution to the inverse Cauchy problem for a fractional differential equation in a Banach space

Kokurin, M. Yu.

doi:10.3103/s1066369x13120037

Cited by 9 publications

(3 citation statements)

References 4 publications

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“…If Condition 1.1 is satisfied, then the problem (1.1) is well-posed [3], in particular, there exists a unique solution u(t), t ∈ [0, T ] for any f ∈ D(A). In [11], we have established the following representation for the solution to (1.1) in terms of functions of the operator −A.…”

Section: Statement Of the Problemmentioning

confidence: 99%

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On a Difference Scheme for Solving Cauchy Problems wuth the Caputo Fractional Derivative in a Banach Space

Kokurin

2017

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We construct and study a time-semidiscretization scheme for the Cauchy problem associated with a linear homogeneous differential equation with the Caputo fractional time derivative of order α ∈ (0, 1) and a spatial sectorial operator in a Banach space. For this scheme, we obtain rate-of-convergence and error estimates in terms of the discretization step. We use properties of Mittag-Leffler functions, hypergeometric functions, and the calculus of sectorial operators in a Banach space. Results of numerical experiments are also reported.

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Section: Statement Of the Problemmentioning

confidence: 99%

“…In accordance with Condition 2.1, we consider G(z) on −K(ϕ 0 ). By the asymptotic expansions from [11;16,Ch.1], it follows that…”

Section: A Finite Difference Approximation For the Fractional Caputo ...mentioning

confidence: 99%

On a Difference Scheme for Solving Cauchy Problems wuth the Caputo Fractional Derivative in a Banach Space

Kokurin

2017

Preprint

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“…A review of publications on this subject can be found in [12][13][14][15][16][17][18][19]. Inverse problems for equations of fractional order in Banach spaces was considered in papers [20,21]. Similar problem was considered for the first order equation (when α = 1) but with a fractional integral in the additional boundary condition [22].…”

Section: Inverse Problemmentioning

confidence: 99%