{"paper":{"title":"An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fernando Olivar-Romero, Oscar Rosas-Ortiz","submitted_at":"2019-05-08T21:05:37Z","abstract_excerpt":"We solve the Cauchy problem defined by the fractional partial differential equation $[\\partial_{tt}-\\kappa\\mathbb{D}]u=0$, with $\\mathbb{D}$ the pseudo-differential Riesz operator of first order, and the initial conditions $u(x,0)=\\mu(\\sqrt{\\pi}x_0)^{-1}e^{-(x/x_0)^2}$, $u_t(x,0)=0$. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse $u(x,0)$ by the Dirac delta distribution $\\varphi(x)=\\mu\\delta(x)$ is obtained as corollary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03343","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}