J Anal https://doi.org/10.1007/s41478-018-0097-2 ORI G INAL RESEARCH PAPER Optimal control of fractional reaction-diffusion equations with Poisson jumps 1 1 N. Durga P. Muthukumar Received: 28 January 2018 / Accepted: 18 May 2018 Forum D’Analystes, Chennai 2018 Abstract This manuscript is concerned with the nonlinear delay fractional reaction- diffusion equations governed by Poisson jumps in Hilbert space. By constructing a suitable measure of non-compactness, the existence of mild solution for the pro- posed problem is proved via ﬁxed point theorem of condensing maps and fractional calculus. Moreover, the existence of optimal control is proved by employing Balder’s theorem. Finally, an example is provided to illustrate the developed theory. Keywords Fractional reaction-diffusion equation Measure of non-compactness Optimal control Poisson jumps Mathematics Subject Classiﬁcation 35K57 35R11 93E20 60G57 1 Introduction Recently, accurate modeling of many dynamical systems leads to a set of fractional differential equations (FDEs). The most important advantage of using fractional (partial) differential equations is their nonlocal property and consequently led to a sustained study of the theory of fractional (partial) differential equations (see [11, 13, 26] and references therein). Reaction-diffusion equations arise naturally in systems consisting of many interacting components like chemical reactions and
The Journal of Analysis – Springer Journals
Published: Jun 4, 2018
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera