On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels
We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag−Leffler kernels. Th...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/9/772 |
| _version_ | 1818194096135602176 |
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| author | Thabet Abdeljawad Arran Fernandez |
| author_facet | Thabet Abdeljawad Arran Fernandez |
| author_sort | Thabet Abdeljawad |
| collection | DOAJ |
| description | We formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag−Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well. |
| first_indexed | 2024-12-12T00:56:51Z |
| format | Article |
| id | doaj.art-cfe29670198e4b718807adf74d41b9c3 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-12T00:56:51Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cfe29670198e4b718807adf74d41b9c32022-12-22T00:43:51ZengMDPI AGMathematics2227-73902019-08-017977210.3390/math7090772math7090772On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler KernelsThabet Abdeljawad0Arran Fernandez1Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaDepartment of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, Cambridge CB3 0WA, UKWe formulate a new class of fractional difference and sum operators, study their fundamental properties, and find their discrete Laplace transforms. The method depends on iterating the fractional sum operators corresponding to fractional differences with discrete Mittag−Leffler kernels. The iteration process depends on the binomial theorem. We note in particular the fact that the iterated fractional sums have a certain semigroup property, and hence, the new introduced iterated fractional difference-sum operators have this semigroup property as well.https://www.mdpi.com/2227-7390/7/9/772discrete fractional calculusAtangana–Baleanu fractional differences and sumsdiscrete Mittag–Leffler functiondiscrete nabla Laplace transformbinomial theoremiterated processdiscrete Dirac delta function |
| spellingShingle | Thabet Abdeljawad Arran Fernandez On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels Mathematics discrete fractional calculus Atangana–Baleanu fractional differences and sums discrete Mittag–Leffler function discrete nabla Laplace transform binomial theorem iterated process discrete Dirac delta function |
| title | On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels |
| title_full | On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels |
| title_fullStr | On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels |
| title_full_unstemmed | On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels |
| title_short | On a New Class of Fractional Difference-Sum Operators with Discrete Mittag-Leffler Kernels |
| title_sort | on a new class of fractional difference sum operators with discrete mittag leffler kernels |
| topic | discrete fractional calculus Atangana–Baleanu fractional differences and sums discrete Mittag–Leffler function discrete nabla Laplace transform binomial theorem iterated process discrete Dirac delta function |
| url | https://www.mdpi.com/2227-7390/7/9/772 |
| work_keys_str_mv | AT thabetabdeljawad onanewclassoffractionaldifferencesumoperatorswithdiscretemittaglefflerkernels AT arranfernandez onanewclassoffractionaldifferencesumoperatorswithdiscretemittaglefflerkernels |