{"id":45036,"date":"2023-09-11T20:20:21","date_gmt":"2023-09-11T12:20:21","guid":{"rendered":"https:\/\/swarma.org\/?p=45036"},"modified":"2023-09-11T20:20:21","modified_gmt":"2023-09-11T12:20:21","slug":"%e5%88%86%e6%95%b0%e9%98%b6%e5%be%ae%e7%a7%af%e5%88%86-%e7%94%9f%e7%89%a9%e5%ad%a6%e7%9a%84%e5%be%ae%e7%a7%af%e5%88%86","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=45036","title":{"rendered":"\u5206\u6570\u9636\u5fae\u79ef\u5206\u2014\u2014\u751f\u7269\u5b66\u7684\u5fae\u79ef\u5206"},"content":{"rendered":"
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\u201c\u6709\u4e9b\u79d1\u5b66\u5bb6\u662f\u767b\u5c71\u8005\u2014\u2014\u4ed6\u4eec\u4e0d\u65ad\u5c06\u81ea\u5df1\u63a8\u5411\u81f3\u9ad8\u70b9\u3002\u5bf9\u6211\u6765\u8bf4\uff0c\u8fd9\u662f\u5360\u4e3b\u5bfc\u7684\uff0c\u6211\u8bd5\u56fe\u6500\u767b\u9ad8\u5cf0\uff0c\u770b\u89c1\u66f4\u591a\u98ce\u666f\u3002\u5176\u4ed6\u79d1\u5b66\u5bb6\u662f\u6d1e\u7a74\u5b66\u5bb6\u2014\u2014\u4ed6\u4eec\u6df1\u5165\u5e7d\u5fae\uff0c\u7a7f\u8fc7\u6ce5\u6cde\uff0c\u6700\u7ec8\u53d1\u73b0\u9690\u85cf\u7684\u5b9d\u85cf\u3002\u201dVassili Kolokoltsov\u8bf4\u9053\u3002<\/span><\/section>\n

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\u767b\u5c71\u548c\u63a2\u7d22\u6d1e\u7a74\u4e4b\u95f4\u7684\u533a\u522b\uff0c\u8ba9 Kolokoltsov \u610f\u8bc6\u5230\u8fd9\u5c31\u50cf\u662f\u4e24\u79cd\u79d1\u5b66\u7814\u7a76\u6a21\u5f0f\u3002\u201c\u8fd9\u4e24\u65b9\u9762\u5728\u79d1\u5b66\u4e2d\u90fd\u975e\u5e38\u91cd\u8981\u3002\u800c\u5206\u6570\u9636\u5fae\u79ef\u5206<\/strong><\/span>\uff08fractional calculus\uff09<\/span>\u4e3a\u4e24\u8005\u90fd\u63d0\u4f9b\u4e86\u53ef\u80fd\u6027\u3002\u201d<\/span><\/section>\n

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\u56fe1. \u79d1\u5b66\u7814\u7a76\u7684\u4e24\u79cd\u65b9\u5f0f\u2014\u2014\u6500\u767b\u9ad8\u5cf0\u548c\u6df1\u5165\u5e7d\u5fae\u3002<\/span><\/section>\n

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\u5173\u4e8e\u5206\u6570\u9636\u5fae\u79ef\u5206\u9886\u57df\u7684\u7814\u7a76\u5174\u8da3\u6700\u8fd1\u5728\u6301\u7eed\u589e\u52a0\uff0c\u56e0\u4e3a\u5206\u6570\u9636\u5fae\u5206\u65b9\u7a0b<\/strong><\/span>\uff08fractional differential equations\uff09<\/span>\u53ef\u4ee5\u7528\u6765\u6a21\u62df\u8bb8\u591a\u590d\u6742\u73b0\u8c61\uff0c\u4ece\u5730\u4e0b\u6c34\u6c61\u67d3\u3001\u5fc3\u810f\u7535\u52a8\u529b\u5b66\uff0c\u5230\u65b0\u6750\u6599\u8bbe\u8ba1\uff0c\u5728\u751f\u7269\u3001\u7269\u7406\u548c\u91d1\u878d\u7b49\u9886\u57df\u6709\u5f88\u591a\u5e94\u7528\u3002<\/span><\/section>\n

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\u201c\u4eba\u4eec\u6700\u521d\u8c08\u8bba\u7684\u662f\u6574\u6570\u3002\u4e4b\u540e\u5728\u67d0\u4e2a\u65f6\u523b\uff0c\u4ed6\u4eec\u610f\u8bc6\u5230\u6574\u6570\u65e0\u6cd5\u63cf\u8ff0\u4e00\u5207\uff0c\u4e8e\u662f\u53d1\u5c55\u51fa\u4e86\u5206\u6570\u3002\u201dKolokoltsov \u89e3\u91ca\u9053\u3002\u7c7b\u4f3c\u5730\uff0c\u4eba\u4eec\u6700\u5f00\u59cb\u5c06\u8fde\u7eed\u7684\u4e58\u6cd5\u63cf\u8ff0\u4e3a\u4e00\u4e2a\u6570\u7684\u6574\u6570\u5e42\u3002\u800c\u4e8b\u5b9e\u8bc1\u660e\uff0c\u5c06\u5176\u6269\u5c55\u5230\u5206\u6570\u5e42\u4e5f\u975e\u5e38\u6709\u7528\uff0c\u4f8b\u5982\u4e00\u4e2a\u6570\u7684\u5e73\u65b9\u6839\u5c31\u662f\u5b83\u76841\/2\u6b21\u5e42\uff0c\u800c\u7acb\u65b9\u6839\u5219\u662f\u5b83\u76841\/3\u6b21\u5e42\u3002<\/span><\/section>\n

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\u5bf9\u4e8e\u6570\u5b66\u8fd0\u7b97\u4e5f\u53ef\u4ee5\u505a\u7c7b\u4f3c\u7684\u4e8b\u60c5\u3002\u5982\u679c\u4f60\u53cd\u590d\u8fdb\u884c\u4e00\u4e2a\u6570\u5b66\u8fd0\u7b97\uff0c\u8fd9\u5c31\u50cf\u5bf9\u8fd0\u7b97\u8fdb\u884c\u6574\u6570\u6b21\u5e42\u7684\u8fd0\u7b97\u3002\u6b63\u5982\u540c\u53ef\u4ee5\u6709\u6570\u7684\u5206\u6570\u5e42\u4e00\u6837\uff0c\u4e5f\u53ef\u4ee5\u6709\u8fd0\u7b97\u7684\u5206\u6570\u5e42\u3002<\/span><\/section>\n

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Kolokoltsov \u548c\u540c\u4e8b\u4eec\u7814\u7a76\u5fae\u79ef\u5206\u8fd0\u7b97\u4e2d\u7684\u5fae\u5206\u548c\u79ef\u5206\uff0c\u5e76\u63a2\u8ba8\u5982\u4f55\u7528\u5fae\u5206\u65b9\u7a0b\u5728\u6570\u5b66\u4e0a\u63cf\u8ff0\u53d8\u5316\u3002\u51e0\u4e2a\u4e16\u7eaa\u4ee5\u6765\uff0c\u5fae\u5206\u65b9\u7a0b\u4e00\u76f4\u662f\u6570\u5b66\u7684\u91cd\u8981\u7ec4\u6210\u90e8\u5206\uff0c\u5bf9\u4e8e\u63cf\u8ff0\u6211\u4eec\u5468\u56f4\u7684\u4e16\u754c\u81f3\u5173\u91cd\u8981\uff0c\u4ece\u63cf\u8ff0\u725b\u987f\u8fd0\u52a8\u5b9a\u5f8b\u5230\u52a8\u7269\u8eab\u4e0a\u7684\u6591\u56fe\u90fd\u6709\u5e94\u7528\u3002<\/span><\/section>\n

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\u5206\u6570\u9636\u5fae\u79ef\u5206\uff0c\u5219\u662f\u4e00\u4e2a\u66f4\u52a0\u590d\u6742\u7684\u6545\u4e8b\u3002\u5206\u6570\u9636\u5fae\u79ef\u5206\u662f\u5bf9\u51fd\u6570\u8fdb\u884c\u975e\u6574\u6570\u9636\u79ef\u5206\u548c\u5fae\u5206\u7684\u5b9a\u91cf\u5206\u6790\u3002\u9636\u6570\u53ef\u4ee5\u662f\u5b9e\u6570\u3001\u590d\u6570\uff0c\u751a\u81f3\u662f\u53d8\u91cf\u7684\u51fd\u6570\u3002\u5173\u4e8e\u975e\u6574\u6570\u9636\u5fae\u5206\u7684\u610f\u4e49\u7684\u7b2c\u4e00\u6b21\u8bb0\u5f55\u51fa\u73b0\u57281695\u5e74\u6d1b\u5fc5\u8fbe<\/span>\uff08Guillaume de l\u2019H\u00f4pital\uff09<\/span>\u5199\u7ed9\u83b1\u5e03\u5c3c\u8328<\/span>\uff08Gottfried Wilhelm Leibniz\uff09<\/span>\u7684\u4e00\u5c01\u4fe1\u4e2d\u3002\u83b1\u5e03\u5c3c\u8328\u4e0e\u725b\u987f\u662f\u540c\u65f6\u4ee3\u4eba\uff0c\u5e76\u4e0e\u4ed6\u5404\u81ea\u72ec\u7acb\u4f46\u5171\u540c\u53d1\u660e\u4e86\u65e0\u7a77\u5c0f\u5fae\u79ef\u5206\u3002\u4ece\u90a3\u65f6\u8d77\uff0c\u8bb8\u591a\u8d21\u732e\u8005\u4e3a\u5206\u6570\u9636\u5fae\u5206\u548c\u79ef\u5206\u63d0\u4f9b\u4e86\u5b9a\u4e49\uff0c\u5206\u6570\u9636\u5fae\u79ef\u5206\u7684\u7406\u8bba\u548c\u5e94\u7528\u5f97\u5230\u4e86\u5f88\u5927\u7684\u6269\u5c55\u3002<\/span><\/section>\n

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\u4e00\u4e2a\u5173\u952e\u6982\u5ff5\u662f\u53cd\u5e38\u6269\u6563<\/span>\uff08anomalous diffusion\uff09<\/span>\u3002\u7ecf\u5178\u7684\u6269\u6563\uff0c\u5982\u91d1\u5c5e\u4e2d\u70ed\u91cf\u7684\u4f20\u64ad\uff0c\u662f\u7528\u5fae\u5206\u65b9\u7a0b\u6765\u63cf\u8ff0\u3002\u7ecf\u5178\u6269\u6563\u7684\u7279\u70b9\u662f\uff0c\u7c92\u5b50\u7684\u4f4d\u79fb\u4e0e\u65f6\u95f4\u4e4b\u95f4\u5b58\u5728\u7ebf\u6027\u5173\u7cfb\u3002\u800c\u5982\u679c\u8fd9\u79cd\u5173\u7cfb\u662f\u975e\u7ebf\u6027\u7684\uff0c\u90a3\u4e48\u5c31\u4f1a\u51fa\u73b0\u53cd\u5e38\u6269\u6563\uff0c\u8fd9\u53ef\u4ee5\u7528\u5206\u6570\u9636\u5fae\u5206\u65b9\u7a0b\u6765\u63cf\u8ff0\u3002<\/span><\/section>\n

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\u5206\u6570\u9636\u601d\u7ef4<\/span>\uff08Fractional-order thinking\uff0cFOT\uff09<\/span>\uff0c\u662f\u4f7f\u7528\u5206\u6570\u9636\u5fae\u79ef\u5206\u8fdb\u884c\u601d\u8003\u7684\u4e00\u79cd\u65b9\u5f0f\u3002\u4f8b\u5982\uff0c\u5728\u6574\u6570\u4e4b\u95f4\u6709\u975e\u6574\u6570\u3002\u5728\u903b\u8f910\u548c\u903b\u8f911\u4e4b\u95f4\uff0c\u6709\u6a21\u7cca\u903b\u8f91\u3002\u8bb8\u591a\u7814\u7a76\u9886\u57df\u90fd\u5305\u542b\u4e86\u5206\u6570\u9636\u601d\u7ef4\uff0c\u4f8b\u5982\uff0c\u81ea\u76f8\u4f3c\u3001\u65e0\u6807\u5ea6\u6216\u6807\u5ea6\u4e0d\u53d8\u6027\u3001\u5e42\u5f8b\u3001\u957f\u7a0b\u76f8\u5173\uff0c\u4ee5\u53ca\u5206\u6570\u566a\u58f01\/f\u03b1<\/span><\/sup>\u3002<\/span><\/section>\n

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\u53c2\u8003\u94fe\u63a5\uff1a<\/span><\/strong><\/span><\/section>\n
[1] https:\/\/plus.maths.org\/content\/calculus-of-the-complex<\/span><\/section>\n
[2] A New Triangle: Fractional Calculus, Renormalization Group, and Machine Learning, https:\/\/asmedigitalcollection.asme.org\/IDETC-CIE\/proceedings-abstract\/IDETC-CIE2021\/85437\/1128150<\/span><\/section>\n

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1. <\/strong>\u590d\u6742\u6027\u7684\u8de8\u5b66\u79d1\u5173\u8054\uff1a\u5206\u6570\u9636\u5fae\u79ef\u5206\u3001\u91cd\u6574\u5316\u7fa4\u4e0e\u673a\u5668\u5b66\u4e60<\/a><\/strong><\/span><\/section>\n
2.<\/strong> \u590d\u6742\u7269\u7406\u5b66\u662f\u53ef\u80fd\u7684\u5417\uff1f\uff5c\u300a\u89c4\u6a21\u6cd5\u5219\u300b\u65b0\u4e66\u8bd5\u8bfb<\/a><\/strong><\/span><\/section>\n
3. <\/strong><\/strong>\u7279\u520a\uff1a\u975e\u7ebf\u6027\u4e0e\u590d\u6742\u7269\u7406\u5b66<\/a><\/strong><\/strong><\/span><\/section>\n
4. <\/strong><\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
5. \u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/a><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/strong><\/span><\/strong><\/span><\/strong><\/section>\n

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