The Blow-Up and Global Existence of Solution to Caputo–Hadamard Fractional Partial Differential Equation with Fractional Laplacian

[1]  Philippe Souplet,et al.  Blow-up in nonlocal reaction-diffusion equations , 1998 .

[2]  T. Cazenave,et al.  An equation whose Fujita critical exponent is not given by scaling , 2008 .

[3]  Hong‐Rui Sun,et al.  The blow-up and global existence of solutions of Cauchy problems for a time fractional diffusion equation , 2015 .

[4]  Nasser-eddine Tatar,et al.  Critical exponents of Fujita type for certain evolution equations and systems with spatio-temporal fractional derivatives , 2005 .

[5]  A. Alsaedi,et al.  Local and blowing‐up solutions for a space‐time fractional evolution system with nonlinearities of exponential growth , 2019, Mathematical Methods in the Applied Sciences.

[6]  F. Weissler Existence and non-existence of global solutions for a semilinear heat equation , 1981 .

[7]  Yanzhi Zhang,et al.  A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem , 2018, J. Comput. Phys..

[8]  A. Kilbas H-Transforms: Theory and Applications , 2004 .

[9]  E. Lenzmann,et al.  Blowup for fractional NLS , 2015, 1509.08845.

[10]  Lei Li,et al.  Cauchy problems for Keller–Segel type time–space fractional diffusion equation , 2017, Journal of Differential Equations.

[11]  Bruno de Andrade,et al.  Regularity theory for a nonlinear fractional reaction–diffusion equation , 2020 .

[12]  Changpin Li,et al.  Asymptotic behaviours of solution to Caputo–Hadamard fractional partial differential equation with fractional Laplacian , 2020, Int. J. Comput. Math..

[13]  H. Kantz,et al.  Continuous-time random walk theory of superslow diffusion , 2010, 1010.0782.

[14]  J. V'azquez,et al.  Blow-up phenomena in nonlocal eigenvalue problems: When theories of L1 and L2 meet , 2020, Journal of Functional Analysis.

[15]  Changpin Li,et al.  Theory and Numerical Approximations of Fractional Integrals and Derivatives , 2019 .

[16]  Keng Deng,et al.  The Role of Critical Exponents in Blow-Up Theorems: The Sequel , 2000 .

[17]  Anatoly N. Kochubei,et al.  Cauchy problem for fractional diffusion equations , 2003 .

[18]  Taekyun Kim,et al.  Identities involving harmonic and hyperharmonic numbers , 2013 .

[19]  M. Kirane,et al.  Qualitative properties of solutions to a time-space fractional evolution equation , 2012 .

[20]  Changpin Li,et al.  Finite Difference Methods for Caputo–Hadamard Fractional Differential Equations , 2020 .

[21]  C. Lomnitz Application of the logarithmic creep law to stress wave attenuation in the solid Earth , 1962 .

[22]  J. Kemppainen,et al.  Positivity of the fundamental solution for fractional diffusion and wave equations , 2019, Mathematical Methods in the Applied Sciences.