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Arab Journal of Basic and Applied Sciences Volume 26, 2019 - Issue 1

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A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

Brajesh Kumar SinghDepartment of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, IndiaCorrespondence[email protected]

http://orcid.org/0000-0003-0121-8274

Mukesh GuptaDepartment of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, India

http://orcid.org/0000-0002-2070-6911

Pages 41-57 | Received 18 Apr 2018, Accepted 13 Oct 2018, Published online: 21 Mar 2019

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https://doi.org/10.1080/25765299.2018.1538067
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Figure 3. The solution behavior of Example 3.3 obtained by using NIPDTM. (a) Comparison of different order solutions with exact solutions for α = β = 2, x = y = z = 1, t ≤ 16. (b) Absolute errors in different order solutions for α = β = 2, x = y = z = 1, t ≤ 1. (c) Absolute errors in 5th order solutions for α = β = 2 y = z = 1, t ≤ 1. (d) Absolute errors in 7th order solutions for α = β = 2, y = z = 1, t ≤ 1.

Table 1. Comparison of absolute errors for α = β = 2 at different time levels $t \leq 1$ .

Display Table

Table 2. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.1 for $α = β = 1.5$ at different time levels $t \leq 1$ .

Display Table

Figure 1. The solution behavior of Example 3.1 obtained by using NIPDTM. (a) Absolute error in 5th order solution for α = β = 2. (b) Absolute error in 7th order solution α = β = 2. (c) Different order solutions for α = β = 2 for large time interval. (d) Sixth order solution for different values of α, β. (e) Eighth order solution for α = β = 2 with x = 1, t ∈ (0, 1). (f) Eighth order solution for α = 1.75, β = 1.85 with x = 1, t ∈ (0, 1).

Figure 2. The solution behavior of Example 3.2 obtained by using NIPDTM. (a) Comparison of different order solutions with exact solutions for α = β = 2, x = y = 1, t ≤ 16. (b) Absolute errors in different order solutions for α = β = 2, x = y = 1, t ≤ 1. (c) Absolute errors in 5th order solutions for α = β = 2, y = 1, t ≤ 1. (d) Absolute errors in 7th order solutions for α = β = 2, y = 1, t ≤ 1. (e) Seventh order solution behavior for α = 1.25, β = 1.5 at t = 1. (f) Seventh order solution behavior for α = 1.5, β = 1.75 at t = 1. (g) Seventh order solution behavior for α = 2, β = 2 at t = 1. (h) Plots of seventh order solutions for different α, β, x = y = 1.

Table 3. Comparison of absolute errors in of example 3.2 for $α = β = 2$ at different time levels $t \leq 1$ .

Display Table

Table 4. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.2 for $α = β = 1.5$ at different time levels $t \leq 1$ .

Display Table

Table 5. Comparison of absolute errors in of example 3.3 for $α = β = 2$ at different time levels $t \leq 1$ .

Display Table

Table 6. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.3 for z = 0.2, $α = β = 1.5$ at different time levels $t \leq 1$ .

Display Table

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A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

Table 1. Comparison of absolute errors for α = β = 2 at different time levels $t \leq 1$ .

Table 2. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.1 for $α = β = 1.5$ at different time levels $t \leq 1$ .

Table 3. Comparison of absolute errors in of example 3.2 for $α = β = 2$ at different time levels $t \leq 1$ .

Table 4. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.2 for $α = β = 1.5$ at different time levels $t \leq 1$ .

Table 5. Comparison of absolute errors in of example 3.3 for $α = β = 2$ at different time levels $t \leq 1$ .

Table 6. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.3 for z = 0.2, $α = β = 1.5$ at different time levels $t \leq 1$ .

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A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods

Figures & data

Table 1. Comparison of absolute errors for α = β = 2 at different time levels t≤1.

Table 2. mth order approximate solutions Sm (m=5,7) of example 3.1 for α=β=1.5 at different time levels t≤1.

Table 3. Comparison of absolute errors in of example 3.2 for α=β=2 at different time levels t≤1.

Table 4. mth order approximate solutions Sm (m=5,7) of example 3.2 for α=β=1.5 at different time levels t≤1.

Table 5. Comparison of absolute errors in of example 3.3 for α=β=2 at different time levels t≤1.

Table 6. mth order approximate solutions Sm (m=5,7) of example 3.3 for z = 0.2, α=β=1.5 at different time levels t≤1.

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Table 1. Comparison of absolute errors for α = β = 2 at different time levels $t \leq 1$ .

Table 2. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.1 for $α = β = 1.5$ at different time levels $t \leq 1$ .

Table 3. Comparison of absolute errors in of example 3.2 for $α = β = 2$ at different time levels $t \leq 1$ .

Table 4. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.2 for $α = β = 1.5$ at different time levels $t \leq 1$ .

Table 5. Comparison of absolute errors in of example 3.3 for $α = β = 2$ at different time levels $t \leq 1$ .

Table 6. mth order approximate solutions $S_{m} (m = 5, 7)$ of example 3.3 for z = 0.2, $α = β = 1.5$ at different time levels $t \leq 1$ .