Matches in SemOpenAlex for { <https://semopenalex.org/work/W3099393693> ?p ?o ?g. }
- W3099393693 endingPage "035003" @default.
- W3099393693 startingPage "035003" @default.
- W3099393693 abstract "Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way to examine the degree of ill-posedness of several classical inverse problems for fractional differential equations involving a Djrbashian-Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm-Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning of related inverse problems, depending crucially on the specific type of given data and quantity of interest. Further, the study exhibits distinct new features of fractional inverse problems." @default.
- W3099393693 created "2020-11-23" @default.
- W3099393693 creator A5039605463 @default.
- W3099393693 creator A5088154743 @default.
- W3099393693 date "2015-02-10" @default.
- W3099393693 modified "2023-10-14" @default.
- W3099393693 title "A tutorial on inverse problems for anomalous diffusion processes" @default.
- W3099393693 cites W1151473480 @default.
- W3099393693 cites W1484979925 @default.
- W3099393693 cites W1485619076 @default.
- W3099393693 cites W1527296550 @default.
- W3099393693 cites W1559113676 @default.
- W3099393693 cites W1559916568 @default.
- W3099393693 cites W1570089119 @default.
- W3099393693 cites W1571050689 @default.
- W3099393693 cites W1574584754 @default.
- W3099393693 cites W1584611818 @default.
- W3099393693 cites W1594234351 @default.
- W3099393693 cites W1597285101 @default.
- W3099393693 cites W162050314 @default.
- W3099393693 cites W1968187902 @default.
- W3099393693 cites W1969312973 @default.
- W3099393693 cites W1970573106 @default.
- W3099393693 cites W1972527756 @default.
- W3099393693 cites W1973950856 @default.
- W3099393693 cites W1978894707 @default.
- W3099393693 cites W1981237273 @default.
- W3099393693 cites W1984160320 @default.
- W3099393693 cites W1989941945 @default.
- W3099393693 cites W1991357707 @default.
- W3099393693 cites W1994338028 @default.
- W3099393693 cites W1998454237 @default.
- W3099393693 cites W2002081567 @default.
- W3099393693 cites W2002245931 @default.
- W3099393693 cites W2004798461 @default.
- W3099393693 cites W2008573113 @default.
- W3099393693 cites W2009426088 @default.
- W3099393693 cites W2011523912 @default.
- W3099393693 cites W2015300527 @default.
- W3099393693 cites W2016680653 @default.
- W3099393693 cites W2017431268 @default.
- W3099393693 cites W2018207223 @default.
- W3099393693 cites W2021834312 @default.
- W3099393693 cites W2025540102 @default.
- W3099393693 cites W2030523557 @default.
- W3099393693 cites W2030765885 @default.
- W3099393693 cites W2034653612 @default.
- W3099393693 cites W2035143701 @default.
- W3099393693 cites W2037793948 @default.
- W3099393693 cites W2041540906 @default.
- W3099393693 cites W2042427812 @default.
- W3099393693 cites W2042819463 @default.
- W3099393693 cites W2043288970 @default.
- W3099393693 cites W2043922553 @default.
- W3099393693 cites W2048060650 @default.
- W3099393693 cites W2051216605 @default.
- W3099393693 cites W2053060970 @default.
- W3099393693 cites W2053518410 @default.
- W3099393693 cites W2053946502 @default.
- W3099393693 cites W2054798928 @default.
- W3099393693 cites W2056738242 @default.
- W3099393693 cites W2062094097 @default.
- W3099393693 cites W2062802638 @default.
- W3099393693 cites W2063879575 @default.
- W3099393693 cites W2065201216 @default.
- W3099393693 cites W2065390423 @default.
- W3099393693 cites W2068501659 @default.
- W3099393693 cites W2072967708 @default.
- W3099393693 cites W2073494671 @default.
- W3099393693 cites W2073878233 @default.
- W3099393693 cites W2076479791 @default.
- W3099393693 cites W2079961897 @default.
- W3099393693 cites W2081531908 @default.
- W3099393693 cites W2081811871 @default.
- W3099393693 cites W2086043021 @default.
- W3099393693 cites W2091313463 @default.
- W3099393693 cites W2093169427 @default.
- W3099393693 cites W2093685032 @default.
- W3099393693 cites W2099130248 @default.
- W3099393693 cites W2105249276 @default.
- W3099393693 cites W2107669040 @default.
- W3099393693 cites W2111271983 @default.
- W3099393693 cites W2123171139 @default.
- W3099393693 cites W2127666079 @default.
- W3099393693 cites W2134837756 @default.
- W3099393693 cites W2141145978 @default.
- W3099393693 cites W2144858695 @default.
- W3099393693 cites W2147905852 @default.
- W3099393693 cites W2165076033 @default.
- W3099393693 cites W2168247726 @default.
- W3099393693 cites W2181344213 @default.
- W3099393693 cites W2219838851 @default.
- W3099393693 cites W2316684568 @default.
- W3099393693 cites W2320258286 @default.
- W3099393693 cites W236966125 @default.
- W3099393693 cites W2561775212 @default.
- W3099393693 cites W2588588830 @default.
- W3099393693 cites W2741903717 @default.