Optimal control of fractional reaction-diffusion equations with Poisson jumps

Optimal control of fractional reaction-diffusion equations with Poisson jumps 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Journal of Analysis Springer Journals

Optimal control of fractional reaction-diffusion equations with Poisson jumps

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Publisher
Springer Singapore
Copyright
Copyright © 2018 by Forum D'Analystes, Chennai
Subject
Mathematics; Analysis; Functional Analysis; Abstract Harmonic Analysis; Special Functions; Fourier Analysis; Measure and Integration
ISSN
0971-3611
eISSN
2367-2501
D.O.I.
10.1007/s41478-018-0097-2
Publisher site
See Article on Publisher Site

Abstract

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

Journal

The Journal of AnalysisSpringer Journals

Published: Jun 4, 2018

References

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