Recently, Shehu has introduced an integral transform called transform, which generalizes the two well-known integrals transforms, i.e. Laplace and Sumudu transform. In literature, many transforms were used to compute solution of integro-differential equations (IDEs). this article, for first time, we use computation $n^{\text{th}}$-order IDEs. We present a general scheme give some examples with ...

Symmetries of nth-order approximate stochastic ordinary differential equations SODEs are studied. The determining equations of these SODEs are derived in an Itô calculus context. These determining equations are not stochastic in nature. SODEs are normally used tomodel nature e.g., earthquakes or for testing the safety and reliability of models in construction engineering when looking at the imp...

The letter presents a technique for Nth-order differentiation of periodic pulse train, which can simultaneously multiply the input repetition rate. This approach uses a single linearly chirped apodized fiber Bragg grating, which grating profile is designed to map the spectral response of the Nth-order differentiator, and the chirp introduces a dispersion that, besides space-to-frequency mapping...

In the current article we present a fast and reliable algorithm for evaluating nth order pentadiagonal determinants in linear time. It is a natural generalization of the DETGTRI algorithm [M. El-Mikkawy, A fast algorithm for evaluating nth order tri-diagonal determinants, J. Comput. Appl. Math. 166 (2004) 581–584]. The algorithm is suited for implementation using computer algebra systems (CAS) ...

We present a formula for the extremes of the null controllable region of a general LTI discrete-time system with bounded inputs. For an nth order system with only real poles (not necessarily distinct), the formula is simpli5ed to an elementary matrix function, which in turn shows that the set of the extremes coincides with a set of trajectories of the time-reversed system under bang–bang contro...