FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Difference methods for solving nonlocal boundary value problems for fractional-order differential convection-diffusion equations with memory effect |
Beshtokov M.KH., KHudalov M.Z. |
2021, issue 1, P. 3-25 DOI: https://doi.org/10.47910/FEMJ202101 |
Abstract |
| In the present paper, in a rectangular domain, we study nonlocal boundary value problems for one-dimensional in space differential equations of convection-diffusion of fractional order with a memory effect, in which the unknown function appears in the differential expression and at the same time appears under the integral sign. The emergence of the integral term in the equation is associated with the need to take into account the dependence of the instantaneous values of the characteristics of the described object on their respective previous values, i.e. the effect of its prehistory on the current state of the system. |
Keywords: Boundary value problems, a priori estimate, differential equation of fractional order, fractional Caputo derivative, convection-diffusion equation, memory effect |
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References |
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