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New Analytical Solutions of Conformable Time Fractional Bad and Good Modified Boussinesq Equations

Hülya Durur

Hülya Durur

Department of Computer Engineering, Faculty of Engineering, Ardahan UniversityArdahan, Turkey
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Durur, Hülya
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Orkun Tasbozan

Orkun Tasbozan

Department of Mathematics, Faculty of Science and Art, Mustafa Kemal UniversityHatay, Turkey
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Tasbozan, Orkun
 and 
Ali Kurt

Ali Kurt

Department of Mathematics, Faculty of Science and Art, Pamukkale UniversityDenizli, Turkey
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Kurt, Ali
  
Apr 10, 2020
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Published Online: Apr 10, 2020
Page range: 447 - 454
Received: May 14, 2019
Accepted: Jun 22, 2019
DOI: https://doi.org/10.2478/amns.2020.1.00042
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© 2020 Hülya Durur et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Solutions of Eq_ (4) with Δ = b2 − 4ac and ε = ±1

Noz(ξ)
1−absech2(a2ξ)b2−ac(1+ɛtanh(a2ξ))2\frac{{ - ab{\text{sec}}{h^2}\left( {\frac{{\sqrt a }}{2}\xi } \right)}}{{{b^2} - ac{{\left( {1 + \varepsilon \tan h\left( {\frac{{\sqrt a }}{2}\xi } \right)} \right)}^2}}}a > 0
2abcsch2(a2ξ)b2−ac(1+ɛcoth(a2ξ))2\frac{{ab{\text{csc}}{h^2}\left( {\frac{{\sqrt a }}{2}\xi } \right)}}{{{b^2} - ac{{\left( {1 + \varepsilon \cot h\left( {\frac{{\sqrt a }}{2}\xi } \right)} \right)}^2}}}a > 0
32asech(aξ)ɛΔ−bsech(aξ)\frac{{2a{\text{sec}}h\left( {\sqrt a \xi } \right)}}{{\varepsilon \sqrt \Delta - b{\text{sec}}h\left( {\sqrt a \xi } \right)}}a > 0, Δ > 0
42asec(−aξ)ɛΔ−bsec(−aξ)\frac{{2a{\text{sec}}\left( {\sqrt { - a} \xi } \right)}}{{\varepsilon \sqrt \Delta - b{\text{sec}}\left( {\sqrt { - a} \xi } \right)}}a < 0, Δ > 0
52acsch(aξ)ɛ−Δ−bcsch(aξ)\frac{{2a{\text{csc}}h\left( {\sqrt a \xi } \right)}}{{\varepsilon \sqrt { - \Delta } - b{\text{csc}}h\left( {\sqrt a \xi } \right)}}a > 0, Δ < 0
62acsc(−aξ)ɛΔ−bcsc(−aξ)\frac{{2a{\text{csc}}\left( {\sqrt { - a} \xi } \right)}}{{\varepsilon \sqrt \Delta - b{\text{csc}}\left( {\sqrt { - a} \xi } \right)}}a < 0, Δ > 0
7−asech2(a2ξ)b+2ɛactanh(a2ξ)\frac{{ - a{\text{sec}}{h^2}\left( {\frac{{\sqrt a }}{2}\xi } \right)}}{{b + 2\varepsilon \sqrt {ac} \tan h\left( {\frac{{\sqrt a }}{2}\xi } \right)}}a > 0, c > 0
8−asec2(−a2ξ)b+2ɛ−actan(−a2ξ)\frac{{ - a{\text{se}}{{\text{c}}^2}\left( {\frac{{\sqrt { - a} }}{2}\xi } \right)}}{{b + 2\varepsilon \sqrt { - ac} \tan \left( {\frac{{\sqrt { - a} }}{2}\xi } \right)}}a < 0, c > 0
9acsch2(a2ξ)b+2ɛaccoth(a2ξ)\frac{{a{\text{csc}}{h^2}\left( {\frac{{\sqrt a }}{2}\xi } \right)}}{{b + 2\varepsilon \sqrt {ac} \cot h\left( {\frac{{\sqrt a }}{2}\xi } \right)}}a > 0, c > 0
10−acsc2(−a2ξ)b+2ɛ−accot(−a2ξ)\frac{{ - a{{\csc }^2}\left( {\frac{{\sqrt { - a} }}{2}\xi } \right)}}{{b + 2\varepsilon \sqrt { - ac} \cot \left( {\frac{{\sqrt { - a} }}{2}\xi } \right)}}a < 0, c > 0
11−ab[1+ɛtanh(a2ξ)] - \frac{a}{b}\left[ {1 + \varepsilon \tan h\left( {\frac{{\sqrt a }}{2}\xi } \right)} \right]a > 0, Δ = 0
12−ab[1+ɛcoth(a2ξ)] - \frac{a}{b}\left[ {1 + \varepsilon \cot h\left( {\frac{{\sqrt a }}{2}\xi } \right)} \right]a > 0, Δ = 0
134aeɛaξ(eɛaξ−b)2−4ac\frac{{4a{e^{\varepsilon \sqrt a \xi }}}}{{{{\left( {{e^{\varepsilon \sqrt a \xi }} - b} \right)}^2} - 4ac}}a > 0
14±4aeɛaξ1−4ace2ɛaξ\frac{{ \pm 4a{e^{\varepsilon \sqrt a \xi }}}}{{1 - 4ac{e^{2\varepsilon \sqrt a \xi }}}}
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