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Title: Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time

Abstract

We prove the correctness of the inverse problem of finding a pair of functions: the classical solution u(x,t) of the first boundary-value problem for a linear diffusion equation with regularized fractional derivative of order α ∈ (1, 2) with respect to time in a rectangular domain (0, ℓ) × (0, t{sub 0}] and unknown initial values of the function u(x,t) for the case of additionally given values of the function at a certain fixed time t{sub 0} .

Authors:
 [1];  [2]
  1. Franko L’viv National University (Ukraine)
  2. “L’vivs’ka Politekhnika” National University (Ukraine)
Publication Date:
OSTI Identifier:
22771554
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Sciences
Additional Journal Information:
Journal Volume: 229; Journal Issue: 2; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; BOUNDARY-VALUE PROBLEMS; DATA; DIFFUSION EQUATIONS; MATHEMATICAL SOLUTIONS; TIME DEPENDENCE

Citation Formats

Lopushans’ka, H. P., and M’yaus, O. M. Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time. United States: N. p., 2018. Web. doi:10.1007/S10958-018-3670-Y.
Lopushans’ka, H. P., & M’yaus, O. M. Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time. United States. doi:10.1007/S10958-018-3670-Y.
Lopushans’ka, H. P., and M’yaus, O. M. Thu . "Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time". United States. doi:10.1007/S10958-018-3670-Y.
@article{osti_22771554,
title = {Restoration of the Initial Data in the Problem for a Diffusion Equation with Fractional Derivative with Respect to Time},
author = {Lopushans’ka, H. P. and M’yaus, O. M.},
abstractNote = {We prove the correctness of the inverse problem of finding a pair of functions: the classical solution u(x,t) of the first boundary-value problem for a linear diffusion equation with regularized fractional derivative of order α ∈ (1, 2) with respect to time in a rectangular domain (0, ℓ) × (0, t{sub 0}] and unknown initial values of the function u(x,t) for the case of additionally given values of the function at a certain fixed time t{sub 0} .},
doi = {10.1007/S10958-018-3670-Y},
journal = {Journal of Mathematical Sciences},
issn = {1072-3374},
number = 2,
volume = 229,
place = {United States},
year = {2018},
month = {2}
}