The inverse source problem for time-fractional diffusion equation: stability analysis and regularization

Figures & data

Figure 1. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.1$ with Example 1: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 2. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.3$ with Example 1: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 3. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.6$ with Example 1: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 4. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.1$ with Example 2: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 5. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.3$ with Example 2: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 6. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.6$ with Example 2: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 7. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.1$ with Example 3: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 8. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.3$ with Example 3: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 9. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.6$ with Example 3: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 10. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.1$ with Example 4: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 11. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.3$ with Example 4: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.

Figure 12. The comparison of the numerical effects between the exact solution and its computed approximations for $p=1$, $\mathit{\alpha }=0.6$ with Example 4: (a) $\mathit{\epsilon }=0.01$, (b) $\mathit{\epsilon }=0.001$.