Geodesic
Numerical-analytical method for solving a boundary-value problem for the modified equation of moisture transfer with time-fractional derivative
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 61-67

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The paper is devoted to a new moisture transfer equation, which generalizes the Aller equation by means the new concept of the fractal rate of change of humidity. This clarifies the presence of water flows directed opposite to the humidity potential. We find a solution of the system of difference equations with constant coefficients obtained by applying the straight-line method to the Aller equation with the Riemann-Liouville time-fractional derivative and first-kind boundary conditions.
Keywords: Aller generalized moisture transfer equation, fractional derivative, straight line method, a priori estimate. 
@article{INTO_2021_198_a5,
     author = {M. A. Kerefov and F. M. Nakhusheva and S.Kh. Gekkieva},
     title = {Numerical-analytical method for solving a boundary-value problem for the modified equation of moisture transfer with time-fractional derivative},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {61--67},
     publisher = {mathdoc},
     volume = {198},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_198_a5/}
}
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M. A. Kerefov; F. M. Nakhusheva; S.Kh. Gekkieva. Numerical-analytical method for solving a boundary-value problem for the modified equation of moisture transfer with time-fractional derivative. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 198 (2021), pp. 61-67. http://geodesic.mathdoc.fr/item/INTO_2021_198_a5/