On a nabla fractional boundary value problem with general boundary conditions

Jagan Mohan Jonnalagadda; Jagan Mohan Jonnalagadda

doi:10.3934/math.2020012

AIMS Mathematics

2020, Volume 5, Issue 1: 204-215. doi: 10.3934/math.2020012

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On a nabla fractional boundary value problem with general boundary conditions

Jagan Mohan Jonnalagadda ^,

Department of Mathematics, Birla Institute of Technology and Science Pilani, Hyderabad-500078, Telangana, India

Received: 02 September 2019 Accepted: 23 October 2019 Published: 29 October 2019
MSC : 26D15, 34A08, 34B05, 39A10, 39A12

In this article, we consider a nabla fractional boundary value problem with general boundary conditions. Brackins & Peterson ^[5] gave an explicit expression for the corresponding Green's function. Here, we show that this Green's function is nonnegative and obtain an upper bound for its maximum value. Since the expression for the Green's function is complicated, derivation of its properties may not be straightforward. For this purpose, we use a few properties of fractional nabla Taylor monomials. Using the Green's function, we will then develop a Lyapunov-type inequality for the nabla fractional boundary value problem.
- nabla fractional difference,
- boundary value problem,
- general boundary conditions,
- Green’s function,
- Lyapunov-type inequality
Citation: Jagan Mohan Jonnalagadda. On a nabla fractional boundary value problem with general boundary conditions[J]. AIMS Mathematics, 2020, 5(1): 204-215. doi: 10.3934/math.2020012

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Abstract

In this article, we consider a nabla fractional boundary value problem with general boundary conditions. Brackins & Peterson ^[5] gave an explicit expression for the corresponding Green's function. Here, we show that this Green's function is nonnegative and obtain an upper bound for its maximum value. Since the expression for the Green's function is complicated, derivation of its properties may not be straightforward. For this purpose, we use a few properties of fractional nabla Taylor monomials. Using the Green's function, we will then develop a Lyapunov-type inequality for the nabla fractional boundary value problem.

References

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