Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy
In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-...
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MDPI AG
2015-05-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/17/5/3172 |
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doaj-38e8564421544f6cb6cc6930424371122020-11-24T23:52:07ZengMDPI AGEntropy1099-43002015-05-011753172318110.3390/e17053172e17053172Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional EntropyRabha W. Ibrahim0Hamid A. Jalab1Institute of Mathematical Sciences, University Malaya, Kuala Lumpur 50603, MalaysiaFaculty of Computer Science and Information Technology, University Malaya, Kuala Lumpur 50603, MalaysiaIn this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus.http://www.mdpi.com/1099-4300/17/5/3172fractional calculusfractional differential equationentropy solution |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rabha W. Ibrahim Hamid A. Jalab |
| spellingShingle |
Rabha W. Ibrahim Hamid A. Jalab Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy Entropy fractional calculus fractional differential equation entropy solution |
| author_facet |
Rabha W. Ibrahim Hamid A. Jalab |
| author_sort |
Rabha W. Ibrahim |
| title |
Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy |
| title_short |
Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy |
| title_full |
Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy |
| title_fullStr |
Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy |
| title_full_unstemmed |
Existence of Ulam Stability for Iterative Fractional Differential Equations Based on Fractional Entropy |
| title_sort |
existence of ulam stability for iterative fractional differential equations based on fractional entropy |
| publisher |
MDPI AG |
| series |
Entropy |
| issn |
1099-4300 |
| publishDate |
2015-05-01 |
| description |
In this study, we introduce conditions for the existence of solutions for an iterative functional differential equation of fractional order. We prove that the solutions of the above class of fractional differential equations are bounded by Tsallis entropy. The method depends on the concept of Hyers-Ulam stability. The arbitrary order is suggested in the sense of Riemann-Liouville calculus. |
| topic |
fractional calculus fractional differential equation entropy solution |
| url |
http://www.mdpi.com/1099-4300/17/5/3172 |
| work_keys_str_mv |
AT rabhawibrahim existenceofulamstabilityforiterativefractionaldifferentialequationsbasedonfractionalentropy AT hamidajalab existenceofulamstabilityforiterativefractionaldifferentialequationsbasedonfractionalentropy |
| _version_ |
1725474844262268928 |