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Theory and Modern Applications

Table 1 The error estimation between the exact and regularized source functions for \(\textrm{x} \in[0,\pi]\)

From: Identifying the space source term problem for a generalization of the fractional diffusion equation with hyper-Bessel operator

\({\textrm{Error}}^{1,2}_{\textrm{m},\textrm {n}}(\upalpha,\upbeta) \)

\(N_{\textrm{x}}=40\), N(p)=10, m = n = 5, c = 0.1, Θ = 0.3

ε:

0.1

0.01

0.001

\({\textrm{Error}}^{1}_{\textrm{m}}(0.1,0.1)\)

 

4.622039876238438

0.813894458788424

0.034641254935990

\({\textrm{Error}}^{2}_{\textrm{n} }(0.1,0.1)\)

 

6.865541133036323

1.307095435681400

0.080884577605506

\({\textrm{Error}}^{1}_{\textrm{m}}(0.5,0.5)\)

 

3.612281616966185

0.661448882414577

0.036340894224658

\({\textrm{Error}}^{2}_{\textrm{n} }(0.5,0.5)\)

 

5.675784647354515

1.121826494146178

0.079463345903329

\({\textrm{Error}}^{1}_{\textrm{m}}(0.9,0.9)\)

 

4.499633069709045

0.994936684930523

0.043721289744985

\({\textrm{Error}}^{2}_{\textrm{n} }(0.9,0.9)\)

 

4.446871112063462

1.090617580396543

0.013012608028477