{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:W3BCCLVMYELOUJUQQGZKPHWWOQ","short_pith_number":"pith:W3BCCLVM","schema_version":"1.0","canonical_sha256":"b6c2212eacc116ea269081b2a79ed6741b088a6f91d7faa348447bb21c5a017f","source":{"kind":"arxiv","id":"1706.03394","version":1},"attestation_state":"computed","paper":{"title":"On Space-Time Fractional Heat Type Non-Homogeneous Time-Fractional Poisson Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ejighikeme McSylvester Omaba","submitted_at":"2017-06-11T19:28:57Z","abstract_excerpt":"Consider the following space-time fractional heat equation with Riemann-Liouville derivative of non-homogeneous time-fractional Poisson process \\begin{eqnarray*} \\partial^\\beta_t u(x,t) =-\\kappa(-\\Delta)^{\\alpha/2} u(x,t) + I_t^{1-\\beta}[\\sigma(u)D_t^\\vartheta N^\\nu_\\lambda(t)], \\,\\, t\\geq 0, \\,x \\in \\mathbb{R}^d, \\end{eqnarray*} where $\\kappa>0, \\,\\,\\beta,\\,\\vartheta\\in(0,1), \\,\\,\\nu\\in(0,1],\\,\\alpha\\in(0,2].$ The operator $D_t^\\vartheta N^\\nu_\\lambda(t) = \\frac{\\rm d}{\\mathrm{d} t} I_t^{1-\\vartheta} N_\\lambda^\\nu(t) = \\frac{\\rm d}{\\mathrm{d} t} \\mathcal{N}_\\lambda^{1-\\vartheta,\\nu}(t)$ with 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Space-Time Fractional Heat Type Non-Homogeneous Time-Fractional Poisson Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ejighikeme McSylvester Omaba","submitted_at":"2017-06-11T19:28:57Z","abstract_excerpt":"Consider the following space-time fractional heat equation with Riemann-Liouville derivative of non-homogeneous time-fractional Poisson process \\begin{eqnarray*} \\partial^\\beta_t u(x,t) =-\\kappa(-\\Delta)^{\\alpha/2} u(x,t) + I_t^{1-\\beta}[\\sigma(u)D_t^\\vartheta N^\\nu_\\lambda(t)], \\,\\, t\\geq 0, \\,x \\in \\mathbb{R}^d, \\end{eqnarray*} where $\\kappa>0, \\,\\,\\beta,\\,\\vartheta\\in(0,1), \\,\\,\\nu\\in(0,1],\\,\\alpha\\in(0,2].$ The operator $D_t^\\vartheta N^\\nu_\\lambda(t) = \\frac{\\rm d}{\\mathrm{d} t} I_t^{1-\\vartheta} N_\\lambda^\\nu(t) = \\frac{\\rm d}{\\mathrm{d} t} \\mathcal{N}_\\lambda^{1-\\vartheta,\\nu}(t)$ with 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