Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform
In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived. Moreover, we also compute the solution of some Cauchy problems and diffusion equations modeled with the HP fra...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/7/5/413 |
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| author | Ved Prakash Dubey Jagdev Singh Sarvesh Dubey Devendra Kumar |
| author_facet | Ved Prakash Dubey Jagdev Singh Sarvesh Dubey Devendra Kumar |
| author_sort | Ved Prakash Dubey |
| collection | DOAJ |
| description | In this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived. Moreover, we also compute the solution of some Cauchy problems and diffusion equations modeled with the HP fractional derivative via Kharrat–Toma transform. The solutions of Cauchy problems and the diffusion equations modeled with the HP fractional derivative are computed in the form of the generalized Mittag–Leffler function. |
| first_indexed | 2024-03-11T03:42:41Z |
| format | Article |
| id | doaj.art-75949c33cfcb42ce95c30679a1408fec |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-11T03:42:41Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-75949c33cfcb42ce95c30679a1408fec2023-11-18T01:26:46ZengMDPI AGFractal and Fractional2504-31102023-05-017541310.3390/fractalfract7050413Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma TransformVed Prakash Dubey0Jagdev Singh1Sarvesh Dubey2Devendra Kumar3Faculty of Mathematical and Statistical Sciences, Shri Ramswaroop Memorial University, Barabanki 225003, Uttar Pradesh, IndiaDepartment of Mathematics, JECRC University, Jaipur 303905, Rajasthan, IndiaDepartment of Physics, L.N.D. College, B.R. Ambedkar Bihar University, Muzaffarpur, Motihari 845401, Bihar, IndiaDepartment of Computer Science and Mathematics, Lebanese American University, Beirut P.O. Box 13-5053, LebanonIn this paper, the Kharrat–Toma transforms of the Prabhakar integral, a Hilfer–Prabhakar (HP) fractional derivative, and the regularized version of the HP fractional derivative are derived. Moreover, we also compute the solution of some Cauchy problems and diffusion equations modeled with the HP fractional derivative via Kharrat–Toma transform. The solutions of Cauchy problems and the diffusion equations modeled with the HP fractional derivative are computed in the form of the generalized Mittag–Leffler function.https://www.mdpi.com/2504-3110/7/5/413Hilfer–Prabhakar fractional derivativeCauchy problemsdiffusion equationsKharrat–Toma transformMittag–Leffler function |
| spellingShingle | Ved Prakash Dubey Jagdev Singh Sarvesh Dubey Devendra Kumar Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform Fractal and Fractional Hilfer–Prabhakar fractional derivative Cauchy problems diffusion equations Kharrat–Toma transform Mittag–Leffler function |
| title | Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform |
| title_full | Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform |
| title_fullStr | Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform |
| title_full_unstemmed | Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform |
| title_short | Analysis of Cauchy Problems and Diffusion Equations Associated with the Hilfer–Prabhakar Fractional Derivative via Kharrat–Toma Transform |
| title_sort | analysis of cauchy problems and diffusion equations associated with the hilfer prabhakar fractional derivative via kharrat toma transform |
| topic | Hilfer–Prabhakar fractional derivative Cauchy problems diffusion equations Kharrat–Toma transform Mittag–Leffler function |
| url | https://www.mdpi.com/2504-3110/7/5/413 |
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