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. 
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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/

[1] Berezin I. S., Zhidkov N. P., Metody vychislenii, v. 2, GIFML, M., 1962

[2] Beshtokov M. Kh., “Differentsialnye i raznostnye kraevye zadachi dlya nagruzhennykh psevdoparabolicheskikh uravnenii tretego poryadka i raznostnye metody ikh chislennoi realizatsii”, Zh. vychisl. mat. mat. fiz., 57:12 (2017), 2021–2041 | MR | Zbl

[3] Beshtokov M. Kh., “Lokalnye i nelokalnye kraevye zadachi dlya vyrozhdayuschikhsya i nevyrozhdayuschikhsya psevdoparabolicheskikh uravnenii s drobnoi proizvodnoi Rimana—Liuvillya”, Differ. uravn., 54:6 (2018), 763–778 | MR | Zbl

[4] Vodakhova V. A., “Kraevaya zadacha s nelokalnym usloviem A. M. Nakhusheva dlya odnogo psevdoparabolicheskogo uravneniya vlagoperenosa”, Differ. uravn., 18:2 (1982), 280–285 | MR | Zbl

[5] Gekkieva S. Kh., Kraevye zadachi dlya nagruzhennykh parabolicheskikh uravnenii s drobnoi proizvodnoi po vremeni, Diss. na soisk. uch. step. kand. fiz.-mat. nauk., Nalchik, 2003

[6] Karsanova Zh. T., Nakhusheva F. M., “Ob odnoi nelokalnoi kraevoi zadache dlya psevdoparabolicheskogo uravneniya tretego poryadka”, Vladikavkaz. mat. zh., 4:2 (2002), 31–37 | MR | Zbl

[7] Kerefov M. A., Kraevye zadachi dlya modifitsirovannogo uravneniya vlagoperenosa s drobnoi po vremeni proizvodnoi, Diss. na soisk. uch. step. kand. fiz.-mat. nauk., Nalchik, 2000

[8] Kerefov M. A., “K voprosu edinstvennosti resheniya nelokalnoi kraevoi zadachi dlya obobschennogo uravneniya vlagoperenosa”, Mat. Vseross. konf. «Ustoichivoe razvitie: problemy, kontseptsii, modeli», posv. 75-letiyu prof. P. M. Ivanova (Nalchik, 16–19 maya 2017 g.), 2017, 102–105

[9] Kerefov M. A., Gekkieva S. Kh., “Nelokalnaya kraevaya zadacha dlya obobschennogo uravneniya vlagoperenosa”, Vestn. Voronezh. un-ta. Ser. Fiz. Mat., 2017, no. 2, 106–112 | Zbl

[10] Kozhanov A. I., “Ob odnoi nelokalnoi kraevoi zadache s peremennymi koeffitsientami dlya uravneniya teploprovodnosti i Allera”, Differ. uravn., 40:6 (2004), 763–774 | MR | Zbl

[11] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973

[12] Makaova R. Kh., “Pervaya kraevaya zadacha v nelokalnoi postanovke dlya obobschennogo uravneniya Allera s drobnoi proizvodnoi Rimana—Liuvillya”, Vestn. Adygeisk. un-ta. Ser. 4. Estestv.-mat. i tekhn. nauki., 2017, no. 4 (211), 36–41

[13] Nakhushev A. M., “O nekotorykh sposobakh linearizatsii uravnenii dvizheniya gruntovykh vod i pochvennoi vlagi”, Kraevye zadachi dlya uravnenii smeshannogo tipa i rodstvennye problemy funktsionalnogo analiza i prikladnoi matematiki, 2, KBGU, Nalchik, 1979, 173–183

[14] Nakhushev A. M., Drobnoe ischislenie i ego primenenie, Fizmatlit, M., 2003

[15] Pskhu A. V., Kraevye zadachi dlya differentsialnykh uravnenii s chastnymi proizvodnymi drobnogo i kontinualnogo poryadka, Izd-vo KBNTs RAN, Nalchik, 2005

[16] Pskhu A. V., Uravneniya v chastnykh proizvodnykh drobnogo poryadka, Nauka, M., 2005

[17] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1989

[18] Soldatov A. P., Shkhanukov M. Kh., “Kraevye zadachi s obschim nelokalnym usloviem A. A. Samarskogo dlya psevdoparabolicheskikh uravnenii vysokogo poryadka”, Dokl. AN SSSR., 297:3 (1987), 547–552

[19] Khubiev K. U., “O matematicheskoi modeli uravneniya Allera”, Vestn. KRAUNTs. Fiz.-mat. nauki., 2016, no. 4-1 (16), 56–65

[20] Chudnovskii A. F., Teplofizika pochv, Nauka, M., 1976

[21] Coleman B. D., Duffin R. J., Mizel V. J., “Instability, uniqueness, and nonexistence theorems for the equation on a strip”, Arch. Rat. Mech. Anal., 1965, no. 19, 100–116 | DOI | Zbl

[22] Yangarber V. A., “The mixed problem for a modified moisture-transfer equation”, J. Appl. Mech. Techn. Phys., 8:1 (1967), 62–64 | DOI