On a nonlocal problem for mixed parabolic–hyperbolic type equation with nonsmooth line of type changing

In this work, we investigate a boundary problem with non-local conditions for mixed parabolic-hyperbolic-type equation with three lines of type changing with Caputo fractional derivative in the parabolic part. We equivalently reduce considered problem to the system of second kind Volterra integral equations. In the parabolic part, we use solution of the first boundary problem with appropriate Green's function, and in hyperbolic parts, we use corresponding solutions of the Cauchy problem.

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“…Regarding the investigations of mixed parabolic-hyperbolic equations with non-smooth lines of type changing we note works [10][11][12][13][14].…”

Section: Formulation Of a Problemmentioning

confidence: 99%

Unique solvability of a non‐local problem for mixed‐type equation with fractional derivative

Karimov

Rakhmatullaeva

2016

Math Methods in App Sciences

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“…Regarding the investigations on parabolic-hyperbolic equations with three lines of type-changing we note works [5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative

2016

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In the present paper, we discuss solvability questions of a non-local problem with integral form transmitting conditions for diffusion-wave equation with the Caputo fractional derivative in a domain bounded by smooth curves. The uniqueness of the solution of the formulated problem we prove using energy integral method with some modifications. The existence of solution will be proved by equivalent reduction of the studied problem into a system of second kind Fredholm integral equations.

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Non-local Boundary Problem with Integral Form Transmitting Condition for Fractional Mixed Type Equation in a Composite Domain

Kerbal

Karimov

Rakhmatullaeva

2017

Math. Model. Nat. Phenom.

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In the present work, we have considered a non-local boundary problem with integral matching conditions for mixed type equation,involving fractional diffusion and wave equations. Using specific algorithm we find solution of considered problem in an explicit form. The proof is based on the method of characteristics, Green's function, Voltera integral equations and solution of a second order ordinary differential equation.

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On a nonlocal problem for mixed parabolic–hyperbolic type equation with nonsmooth line of type changing

Cited by 5 publications

References 9 publications

Unique solvability of a non‐local problem for mixed‐type equation with fractional derivative

Unique solvability of a non‐local problem for mixed‐type equation with fractional derivative

Solvability of a Non-local Problem with Integral Transmitting Condition for Mixed Type Equation with Caputo Fractional Derivative

Non-local Boundary Problem with Integral Form Transmitting Condition for Fractional Mixed Type Equation in a Composite Domain

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