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On discrete sequential fractional boundary value problems. (English) Zbl 1236.39008

The author considers several different types of discrete sequential fractional boundary value problems. Our prototype equation is \[ -\Delta^{\mu_1}\Delta^{\mu_2} \Delta^{\mu_3} y(t)= f(t+ \mu_1+ \mu_2+ \mu_3-1,\,y(t+ \mu_1+ \mu_2+ \mu_3- 1)) \] subject to the conjugate boundary conditions \(y(0)= 0= y(b+ 2)\), where \[ f: [1,b+1]_{N_0}\times R\to[0,+\infty) \] is a continuous function and \(\mu_1,\mu_2,\mu_3\in (0,1)\) satisfy \(1< \mu_1+ \mu_3< 2\) and \(1< \mu_1+ \mu_2+ \mu_3< 2\). He also obtains results for delta-nabla discrete fractional boundary value problems. As an application of our analysis, he gives conditions under which such problem will admit at least one positive solution.

MSC:

39A12 Discrete version of topics in analysis
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