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Fractional Bloch equation with delay

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dc.contributor.author Bhalekar, Sachin
dc.contributor.author Daftardar-Gejji, Varsha
dc.contributor.author Baleanu, Dumitru
dc.contributor.author Magin, Richard
dc.date.accessioned 2017-02-17T07:30:44Z
dc.date.available 2017-02-17T07:30:44Z
dc.date.issued 2011-03
dc.identifier.citation Bhalekar, S...et al. (2011). Fractional Bloch equation with delay. Computers&Mathematics With Applications, 61(5), 1355-1365. http://dx.doi.org/ 10.1016/j.camwa.2010.12.079 tr_TR
dc.identifier.issn 0898-1221
dc.identifier.uri http://hdl.handle.net/20.500.12416/1262
dc.description.abstract In this paper we investigate a fractional generalization of the Bloch equation that includes both fractional derivatives and time delays. The appearance of the fractional derivative on the left side of the Bloch equation encodes a degree of system memory in the dynamic model for magnetization. The introduction of a time delay on the right side of the equation balances the equation by also adding a degree of system memory on the right side of the equation. The analysis of this system shows different stability behavior for the T(1) and the T(2) relaxation processes. The T(1) decay is stable for the range of delays tested (1-100 mu s), while the T(2) relaxation in this model exhibited a critical delay (typically 6 mu s) above which the system was unstable. Delays are expected to appear in NMR systems, in both the system model and in the signal excitation and detection processes. Therefore, by including both the fractional derivative and finite time delays in the Bloch equation, we believe that we have established a more complete and more realistic model for NMR resonance and relaxation tr_TR
dc.language.iso eng tr_TR
dc.publisher Pergamon-Elsevier Science Ltd tr_TR
dc.relation.isversionof 10.1016/j.camwa.2010.12.079 tr_TR
dc.rights info:eu-repo/semantics/closedAccess
dc.subject Fractional Calculus tr_TR
dc.subject Bloch Equation tr_TR
dc.subject Delay tr_TR
dc.title Fractional Bloch equation with delay tr_TR
dc.type article tr_TR
dc.relation.journal Computers&Mathematics With Applications tr_TR
dc.identifier.volume 61 tr_TR
dc.identifier.issue 5 tr_TR
dc.identifier.startpage 1355 tr_TR
dc.identifier.endpage 1365 tr_TR
dc.contributor.department Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü tr_TR


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