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- W2022067970 abstract "This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the solution. Then the structure of the solutions space is discussed, and, in a particular case, an explicit form of the general solution involving discrete analogues of Mittag-Leffler functions is presented. All our observations are performed on a special time scale which unifies and generalizes ordinary difference calculus and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>q</mml:mi></mml:math>-difference calculus. Some of our results are new also in these particular discrete settings." @default.
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- W2022067970 date "2011-01-01" @default.
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- W2022067970 title "Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations" @default.
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- W2022067970 doi "https://doi.org/10.1155/2011/565067" @default.
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