A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation
We discuss on integrable solutions for a generalized Henry-type integral inequality in which weak singularity and delays are involved. Not requiring continuity or differentiability for some given functions, we use a modified iteration argument to give an estimate of the unknown function in terms of...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/841718 |
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| _version_ | 1832549695262556160 |
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| author | Jun Zhou |
| author_facet | Jun Zhou |
| author_sort | Jun Zhou |
| collection | DOAJ |
| description | We discuss on integrable solutions for a generalized Henry-type integral inequality in which weak singularity and delays are involved. Not requiring continuity or differentiability for some given functions, we use a modified iteration argument to give an estimate of the unknown function in terms of the multiple Mittag-Leffler function. We apply the result to give
continuous dependence of solutions on initial data, derivative orders, and known functions for a fractional differential equation. |
| format | Article |
| id | doaj-art-feb8f2d6aa2f4110af9758c1ee88765a |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-feb8f2d6aa2f4110af9758c1ee88765a2025-02-03T06:10:51ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/841718841718A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential EquationJun Zhou0Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, ChinaWe discuss on integrable solutions for a generalized Henry-type integral inequality in which weak singularity and delays are involved. Not requiring continuity or differentiability for some given functions, we use a modified iteration argument to give an estimate of the unknown function in terms of the multiple Mittag-Leffler function. We apply the result to give continuous dependence of solutions on initial data, derivative orders, and known functions for a fractional differential equation.http://dx.doi.org/10.1155/2014/841718 |
| spellingShingle | Jun Zhou A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation Journal of Applied Mathematics |
| title | A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation |
| title_full | A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation |
| title_fullStr | A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation |
| title_full_unstemmed | A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation |
| title_short | A Generalized Henry-Type Integral Inequality and Application to Dependence on Orders and Known Functions for a Fractional Differential Equation |
| title_sort | generalized henry type integral inequality and application to dependence on orders and known functions for a fractional differential equation |
| url | http://dx.doi.org/10.1155/2014/841718 |
| work_keys_str_mv | AT junzhou ageneralizedhenrytypeintegralinequalityandapplicationtodependenceonordersandknownfunctionsforafractionaldifferentialequation AT junzhou generalizedhenrytypeintegralinequalityandapplicationtodependenceonordersandknownfunctionsforafractionaldifferentialequation |