A study on partial dynamic equation on time scales involving derivatives of polynomials

Author name not available (Why is that?)

Publication date: 2 August 2016

Abstract: Let

m a t h b f P_{b}^{m} (x)

be a

2 m + 1 -

degree integer-valued polynomial in

x, b

. Let be a two-dimensional time scale

L a m b d a^{2} = m a t h b b T_{1} i m e s m a t h b b T_{2} = t = (x, b) c o l o n; x i n m a t h b b T_{1},; b i n m a t h b b T_{2}

. Let be

m a t h b b T_{1} = m a t h b b T_{2}

. In this manuscript we derive and discuss the following partial dynamic equation on time scales. For every

t i n m a t h b b T_{1},; x, b i n L a m b d a^{2},; m = c o n s t,; m i n m a t h b b N

[ (t^{2m+1})^{Delta} = frac{partial mathbf{P}_b^m(x)}{Delta x} �igg |_{x = t, ; b = sigma(t)} + frac{partial mathbf{P}_b^m(x)}{Delta b}�igg |_{x = t, ; b = t}, ] where

s i g m a (t) > t

is forward jump operator. In addition, we discuss various derivative operators in context of partial cases of above equation, we show finite difference, classical derivative,

q -

derivative,

q -

power derivative on behalf of it.

Has companion code repository: https://github.com/kolosovpetro/astudyondynamicequations

Mathematics Subject Classification ID

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