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Solutions to a discrete right-focal fractional boundary value problem
C S Goodrich
- Vol. 5, Iss: 2, pp 195-216
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TLDR
In this paper, a well-posed discrete right-focal fractional boundary value problem was introduced, where the order ν of the fractional difference satisfies 1 < ν ≤ 2.Abstract:
In this paper, we introduce a well-posed discrete right-focal fractional boundary value problem in the case where the order ν of the fractional difference satisfies 1 < ν ≤ 2. We deduce Green’s function for this problem and prove certain properties about Green’s function. We show in the case ν = 2 that our results agree with the previously known results for second-order discrete boundary value problems but that new results are obtained if 1 < ν < 2. In particular, we show that in great contrast to the case when ν = 2, Green’s function is not monotone in the case when 1 < ν < 2. Finally, we deduce some conditions under which positive solutions to the boundary value problem exist as well as some conditions under which the boundary value problem will have a unique solution. AMS Subject Classifications: Primary: 26A33, 39A05, 39A12; Secondary: 33B15, 47H10.read more
Citations
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Existence and uniqueness of solutions to a fractional difference equation with nonlocal conditions
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On discrete sequential fractional boundary value problems
TL;DR: In this paper, the authors analyzed several different types of discrete sequential fractional boundary value problems and gave conditions under which such problems will admit at least one positive solution under conjugate boundary conditions.
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Existence of a positive solution to systems of differential equations of fractional order
TL;DR: The results here generalize some recent results on both scalar fractional boundaries value problems and systems of fractional boundary value problems, and provide two explicit numerical examples to illustrate the generalizations that the results afford.
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Existence of a positive solution to a system of discrete fractional boundary value problems
TL;DR: Some recent results both on discrete fractional boundary value problems and on discrete integer-order boundaryvalue problems are generalized, and the techniques provide new results in each case.
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On a discrete fractional three-point boundary value problem
TL;DR: In this paper, a discrete fractional three-point boundary value problem (BVP) was studied, and it was shown that the range of admissible boundary conditions depends upon the order of the difference equation.
References
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TL;DR: In the beginning, when having significantly cash, why don't you attempt to acquire something basic in the beginning? That's something that will guide you to understand even more in the region of the globe, experience, some places, history, amusement, and a lot more as discussed by the authors.
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