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Ali, Muhammad; Malik, Salman A.

An inverse problem for a family of two parameters time fractional diffusion equations with nonlocal boundary conditions. (English) Zbl 1387.80006

Math. Methods Appl. Sci. 40, No. 18, 7737-7748 (2017).
Summary: The determination of a space-dependent source term along with the solution for a 1-dimensional time fractional diffusion equation with nonlocal boundary conditions involving a parameter \(\beta>0\) is considered. The fractional derivative is generalization of the Riemann-Liouville and Caputo fractional derivatives usually known as Hilfer fractional derivative. We proved existence and uniqueness results for the solution of the inverse problem while over-specified datum at 2 different time is given. The over-specified datum at 2 time allows us to avoid initial condition in terms of fractional integral associated with Hilfer fractional derivative.

Cited in 5 Documents

MSC:

80A23 Inverse problems in thermodynamics and heat transfer
65N21 Numerical methods for inverse problems for boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
45J05 Integro-ordinary differential equations
34K37 Functional-differential equations with fractional derivatives
42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series

Keywords:

bi-orthogonal system of functions; Hilfer fractional derivative; Mittag-Leffler function; nonlocal boundary conditions
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References:

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