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• W2425743575 abstract "We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form begin{equation*} left{ begin{array}{rll} Delta^{alpha} u(n) &= Au(n+2) + f(n,u(n)), quad n in mathbb{N}_0, ,, 1< alpha leq 2; u(0) &= u_0; u(1) &= u_1, end{array} right. end{equation*} where $A$ is an closed linear operator defined on a Banach space $X$. Our ideas are inspired on the Poisson distribution as a tool to sampling fractional differential operators into fractional differences. Using our abstract approach, we are able to show existence and uniqueness of solutions for the problem (*) on a distinguished class of weighted Lebesgue spaces of sequences, under mild conditions on strongly continuous sequences of bounded operators generated by $A,$ and natural restrictions on the nonlinearity $f$. Finally we present some original examples to illustrate our results." @default.
• W2425743575 created "2016-06-24" @default.
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• W2425743575 date "2016-06-16" @default.
• W2425743575 modified "2023-09-27" @default.
• W2425743575 title "On well-posedness of vector-valued fractional differential-difference equations" @default.
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• W2425743575 hasPublicationYear "2016" @default.
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