• First Order Solution

*<sup>u</sup>*1, 1 <sup>=</sup> <sup>2</sup>(*h*2−*h*1) <sup>α</sup><sup>4</sup> (*h*<sup>1</sup> − *h*<sup>2</sup> − *h*1α + *y*α) 4*h*<sup>2</sup> 1*nK*<sup>3</sup> 0, 1 − <sup>8</sup>*h*1*h*2*nK*<sup>3</sup> 0, 1 + <sup>4</sup>*h*<sup>2</sup> 2*nK*<sup>3</sup> 0, 1 −*K*1, 1α<sup>2</sup> + <sup>4</sup>(*h*2−*h*1) 6*n* α(−*h*1+*h*2+*h*1α−*y*α) 2 (ln[*h*1−*h*2] − ln[(*h*1−*h*2)(1+α)]) <sup>3</sup> *K*<sup>3</sup> 0, 1 + <sup>24</sup>(*h*2−*h*1) 5*n* <sup>α</sup>2(−*h*1+*h*2+*h*1α−*y*α)(ln[*h*1−*h*2]−ln[(*h*1−*h*2)(1+α)]) <sup>2</sup> *K*<sup>3</sup> 0, 1 <sup>−</sup> <sup>2</sup>(*h*2−*h*1) *<sup>C</sup>*<sup>1</sup> α4 - (1+α) 2 (ln[*h*1−*h*2]−ln[(*h*1−*h*2)(α+1)]) 3 (ln[*h*2−*h*1]−ln[(*h*2−*h*1)(1+α)]) × *K*3 0, 1 <sup>+</sup> <sup>1</sup> α4 - (1+α) 2 (ln[*h*1−*h*2]−ln[(*h*1−*h*2)(1+α)]) 3 (ln[*h*2−*h*1]−ln[(*h*2−*h*1)(1+α)]) 2(−*h*<sup>1</sup> + *h*2) - (−*h*<sup>1</sup> + *h*2) --*K*3 0, 1*C*<sup>2</sup> + *K*1, 1*C*<sup>3</sup> ln[*h*<sup>2</sup> − *h*1] + - *K*3 0, 1*C*<sup>4</sup> + *K*1, 1*C*<sup>5</sup> (1 + α) <sup>2</sup> ln[(*h*<sup>2</sup> <sup>−</sup> *<sup>h</sup>*1)(<sup>1</sup> <sup>+</sup> <sup>α</sup>)] (29) σ<sup>1</sup> = 0 (30)

here,

$$K\_{0,1} = \frac{(1+d+h\_2-Q-h\_1)\mathfrak{a}^2(\ln[h\_2-h\_1]-\ln[(h\_2-h\_1)(1+\mathfrak{a})])}{(-h\_2+h\_1)^3(2\mathfrak{a}+(\mathfrak{a}+2)\ln[h\_2-h\_1]-(2+\mathfrak{a})\ln[(h\_2-h\_1)(1+\mathfrak{a})])}\tag{31}$$

$$\omega\_{\chi} = (\omega\_1, \omega\_2, \omega\_3)\mathfrak{a}(\ln[h\_1-h\_1]-\ln[h\_2-h\_1](1+\mathfrak{a})])\omega$$

$$\begin{array}{ll} K\_{1,1} = & -\left( (1+d-Q)\alpha^2 (\ln[h\_1-h\_2] - \ln[(h\_1-h\_2)(1+\alpha)]) \right) / \\ & \left( (h\_1-h\_2)^2 (-2h\_1\alpha + 2h\_2\alpha + (h\_1+h\_2)\alpha\ln[h\_1-h\_2] - \\ & 2(h\_1-h\_2+h\_1\alpha)\ln[-h\_1+h\_2] - h\_1\alpha\ln[(h\_1-h\_2)(1+\alpha)] - \\ & h\_2\alpha\ln[(h\_1-h\_2)(1+\alpha)] + 2h\_1\ln[(-h\_1+h\_2)(1+\alpha)] - \\ & 2h\_2\ln[(-h\_1+h\_2)(1+\alpha)] + 2h\_1\alpha\ln[(-h\_1+h\_2)(1+\alpha)] ) \end{array} \tag{32}$$

In above-presented equations, *C*1–*C*<sup>5</sup> are some lengthy calculations that have particular values by considering above-given boundary conditions and are defined in Appendix A.
