Approximate solution for a 2-D fractional differential equation with discrete random noise

Semilinear parabolic diffusion systems on the sphere with Caputo-Fabrizio operator

“…Partial diferential equations on the sphere and their analysis were investigated by many authors, such as many authors, for example [13,14,15,16,17,9,12,33,34,35,22,28]. These equations play a role in modeling a number of physical phenomena that occur in the earth's surface or in earthquakes and seismic events.…”

Identical approximation operator and regularization method for the Cauchy problem of 2‐D heat conduction equation

“…A mathematical model for a physical phenomena is ill‐posed or improperly posed in the concept of Hadamard 3 if one of the properties, that is, existence, uniqueness, and stability, is not satisfied. Different mathematical models and approaches for the ill‐posed problems have been researched 4–7 …”

“…Different mathematical models and approaches for the ill-posed problems have been researched. [4][5][6][7] In many industrial heat transfer situations, one wishes to determine the temperature from transient temperature measurement at one or more interior locations. Over the last decades, many researchers were interested into the inverse heat conduction problem (IHCP), which is to estimate a surface condition from interior measurements.…”

On a nonlocal problem for parabolic equation with time dependent coefficients

“…The positional results and methods for the ODE and PDEs models are not the same and completely different. In order for the reader to have more access to this kind of fractional diffusion equations with conformable derivative, we refer to [2,[6][7][8][9][10][11][12][13][14][15][16][17]. In addition, we can find the topics of initial and final problems, which are studied by many authors, in [18][19][20][21][22][23][24][25][26][27].…”