Resolvents for weakly singular kernels and fractional differential equations (Q435054)
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scientific article; zbMATH DE number 6057268
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Resolvents for weakly singular kernels and fractional differential equations |
scientific article; zbMATH DE number 6057268 |
Statements
Resolvents for weakly singular kernels and fractional differential equations (English)
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16 July 2012
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singular integral equations
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Volterra equations
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Abel integral equations
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fractional differential equations
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resolvents
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weakly singular kernels
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The resolvent matrix equation NEWLINE\[NEWLINE R(t,s) = B(t,s) + \int\limits_s^t B(t,u) R(u,s) du, NEWLINE\]NEWLINE where \(B(t,s)\) denotes a given weakly singular matrix is studied. The solution \(R(t,s)\) is obtained by means of fixed point mappings. The result is a series that begins with some singular terms after which the remainder of the terms defines a continuous function. The result is employed to obtain the resolvent of the kernel of the generalized Abel integral equation of the second kind.
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