On a problem for the loaded degenerating mixed type equation involving integral-differential operators
https://doi.org/10.17586/2220-8054-2017-8-3-323-333
Abstract
This work aims to study the existence and uniqueness of a solution for a problem of the loaded degenerating mixed type equation. We consider the loaded parabolic-hyperbolic equation involving the Caputo fractional derivative and Riemann-Liouville integrals. The uniqueness of solution is proved by using the method of integral energy applying an extremum principle. Based on the statement of equivalence between “The existence and uniqueness of solution” and “Solvability of the respectively Fredholm type integral equations”, the existence of a solution was proved.
Keywords
loaded degenerating equation,
parabolic-hyperbolic type,
integral operators,
Caputo fractional derivative,
existence and uniqueness of solution,
integral equations
Supporting agencies: The authors are grateful to the reviewers for useful suggestions which improve the contents of this paper.
About the Authors
B. I. Islomov
National University of Uzbekistan
Uzbekistan
Uzbekistan
Universitetskaya-4, VUZgorodog, Tashkent, 100174
O. Kh. Abdullayev
National University of Uzbekistan
Uzbekistan
Uzbekistan
Universitetskaya-4, VUZgorodog, Tashkent, 100174
N. K. Ochilova
Tashkent financial institute
Uzbekistan
Uzbekistan
st. Amir Timur. 57, Tashkent, 100000
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Review
For citations:
Islomov B.I., Abdullayev O.Kh., Ochilova N.K. On a problem for the loaded degenerating mixed type equation involving integral-differential operators. Nanosystems: Physics, Chemistry, Mathematics. 2017;8(3):323-333. https://doi.org/10.17586/2220-8054-2017-8-3-323-333
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