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On an initial value problem for time fractional pseudo-parabolic equation with Caputo derivative. (English) Zbl 07924844


MSC:

26A33 Fractional derivatives and integrals
35B65 Smoothness and regularity of solutions to PDEs
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35R11 Fractional partial differential equations
Full Text: DOI

References:

[1] PodlubnyI. Fractional Differential Equations. California: Academic press; 1999. · Zbl 0924.34008
[2] KiryakovaV. Generalized Fractional Calculus and Applications Pitman Research Notes in Mathematics 301. Harlow: Longman; 1994. · Zbl 0882.26003
[3] SunHG, ZhangY, BaleanuD, ChenW, ChenYQ. A new collection of real world applications of fractional calculus in science and engineering. Commun Nonlinear Sci Numer Simul. 2018;64:213‐231. · Zbl 1509.26005
[4] LiL, LiuGJ. A generalized definition of Caputo derivatives and its application to fractional ODEs. SIAM J Math Anal. 2018;50(3):2867‐2900. · Zbl 1401.26013
[5] BarenblatGI, KochivaI. Basic concepts in the theory of seepage of homogeneous liquids in fissured rock. J Appl Math Mech. 1960;24(5):1286‐1303. · Zbl 0104.21702
[6] BenjaminTB, BonaJL, MahonyJJ. Model equations for long waves in nonlinear dispersive systems. Philos Trans R Soc Lond Ser A. 1972;272:47‐78. · Zbl 0229.35013
[7] TingWT. Certain non‐steady flows of second‐order fluids. Arch Ration Mech Anal. 1963;14:1‐26. · Zbl 0139.20105
[8] PadronV. Effect of aggregation on population recovery modeled by a forward‐backward pseudoparabolic equation. Trans Am Math Soc. 2004;356:2739‐2756. · Zbl 1056.35103
[9] CaoY, YinJ, WangC. Cauchy problems of semilinear pseudo‐parabolic equations. J Differ Equ. 2009;246:4568‐4590. · Zbl 1179.35178
[10] CaoY, LiuC. Initial boundary value problem for a mixed pseudo‐parabolic p‐Laplacian type equation with logarithmic nonlinearity. Electron J Differ Equ. 2018;2018(116):1‐19. · Zbl 1391.35230
[11] HuafeiD, YadongS, XiaoxiaoZ. Global well‐posedness for a fourth order pseudo‐parabolic equation with memory and source terms. Disc Contin Dyn Syst, Ser B. 2016;21(3):781‐801. · Zbl 1331.35204
[12] ChenH, XuH. Global existence and blow‐up in finite time for a class of finitely degenerate semilinear pseudo‐parabolic equations. Acta Math Sin Engl Ser. 2019;35(7):1143‐1162. · Zbl 1417.35063
[13] ChenH, XuH. Global existence and blow‐up of solutions for infinitely degenerate semilinear pseudo‐parabolic equations with logarithmic nonlinearity. Discret Contin Dyn Syst. 2019;39(2):1185‐1203. · Zbl 1404.35233
[14] ChenH, TianS. Initial boundary value problem for a class of semilinear pseudo‐parabolic equations with logarithmic nonlinearity. J Differ Equ. 2015;258(12):4424‐4442. · Zbl 1370.35190
[15] DingH, ZhouJ. Global existence and blow‐up for a mixed pseudo‐parabolic p‐Laplacian type equation with logarithmic nonlinearity. J Math Anal Appl. 2019;478:393‐420. · Zbl 1447.35202
[16] HeY, GaoH, WangH. Blow‐up and decay for a class of pseudo‐parabolic p‐Laplacian equation with logarithmic nonlinearity. Comput Math Appl. 2018;75(2):459‐469. · Zbl 1409.35126
[17] JinL, LiL, FangS. The global existence and time‐decay for the solutions of the fractional pseudo‐parabolic equation. Comput Math Appl. 2017;73(10):2221‐2232. · Zbl 1386.35443
[18] LuY, FeiL. Bounds for blow‐up time in a semilinear pseudo‐parabolic equation with nonlocal source. J Inequalities Appl. 2016;2016:229. · Zbl 1346.60096
[19] SunF, LiuL, WuY. Global existence and finite time blow‐up of solutions for the semilinear pseudo‐parabolic equation with a memory term. Applicable Analysis. 2019;98(4):735‐755. nonlocal term, Math. Meth. Appl. Sci., Vol. 39, Iss. 13 (2016), pp. 3591-3606. · Zbl 1407.35122
[20] ZhuX, LiF, LiY. Global solutions and blow up solutions to a class of pseudo‐parabolic equations with nonlocal term. Appl Math Comput. 2018;329:38‐51. · Zbl 1427.35148
[21] SinghJ, KumarD, BaleanuD. A new analysis of fractional fish farm model associated with Mittag‐Leffler‐type kernel. Int J Biomath. 2020;13(2):2050010. · Zbl 1442.34131
[22] SinghJ, JassimHK, KumarD. An efficient computational technique for local fractional Fokker Planck equation. Physica A: Stat Mech Appl. 2020;555:124525. · Zbl 1496.65193
[23] SinghJ, KumarD, KumarS. An efficient computational method for local fractional transport equation occurring in fractal porous media. Comp Appl Math. 2020;39:137. · Zbl 1463.76050
[24] SousaCVJ, deOliveiraCE. Fractional order pseudoparabolic partial differential equation: Ulam‐Hyers stability. Bull Braz Math Soc (NS). 2019;50(2):481‐496. · Zbl 1415.35284
[25] BeshtokovMK. To boundary‐value problems for degenerating pseudoparabolic equations with Gerasimov‐Caputo fractional derivative. Izv Vyssh Uchebn Zaved Mat. 2018;10:3‐16.
[26] BeshtokovMK. Boundary‐value problems for loaded pseudoparabolic equations of fractional order and difference methods of their solving. Russ Math. 2019;63:1‐10. Springer. · Zbl 1429.35196
[27] BeshtokovMK. Boundary value problems for a pseudoparabolic equation with the Caputo fractional derivative. Diff Equ. 2019;55(7):884‐893. · Zbl 1426.35221
[28] ArendtW, Ter ElstAFM, WarmaM. Fractional powers of sectorial operators via the Dirichlet‐to‐Neumann operator. Comm Partial Diff Equ. 2018;43(1):1‐24.
[29] KilbasAA, SrivastavaHM, TrujilloJJ. Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier Science B.V.; 2006. · Zbl 1092.45003
[30] Gopala RaoVR, TingTW. Solutions of pseudo‐heat equations in the whole space. Arch Ration Mech Anal. 1972;49:57‐78. · Zbl 0255.35049
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