In this paper, we consider the n-term linear fractional-order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by Adomian decomposition method. With the equivalent transmutation, we show that the solution by Adomian decomposition method is the same as the solution by the Green's function. Finally, we illustrate our result with some examples.
The performance of biodiesel in a single-cylinder diesel engine was studied and optimized by varying the engine settings, including the injection timing, injection pressure, and fuel pump plunger diameter. The engine emissions were found to be lowered for particulate matters (PM) and hydrocarbon (HC) with the use of biodiesel, but an obvious increase in the oxides of nitrogen (NOx) was observed, particularly at high engine loadings. The results revealed that individual adjustment of the above-mentioned parameters could not acquire a good balance between PM and NOx emissions. On the other hand, multiparameter engine adjustment with the consideration of their cross-interactive effects can keep the benefit of reducing PM and HC without increasing NOx emission and sacrificing fuel combustion efficiency.
We prove several basic properties for difference ascending chains including a necessary and sufficient condition for an ascending chain to be the characteristic set of its saturation ideal and a necessary and sufficient condition for an ascending chain to be the characteristic set of a reflexive prime ideal. Based on these properties, we propose an algorithm to decompose the zero set of a finite set of difference polynomials into the union of zero sets of certain ascending chains. This decomposition algorithm is implemented and used to solve the perfect ideal membership problem and to prove certain difference identities automatically.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.