# 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:

- Franko L’viv National University (Ukraine)
- “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}

}

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