Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative

Jagdish Ashruba Nanware

doi:doi:10.11648/j.pamj.20211002.11

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Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative

Jagdish Ashruba Nanware

Published in Pure and Applied Mathematics Journal (Volume 10, Issue 2)

Received: 26 January 2021 Accepted: 14 February 2021 Published: 26 March 2021

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Abstract

In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.

Published in	Pure and Applied Mathematics Journal (Volume 10, Issue 2)
DOI	10.11648/j.pamj.20211002.11
Page(s)	38-48
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Existence and Uniqueness, Sequential Fractional Differential Equations, Lower and Upper Solutions, Monotone Technique

References

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Jagdish Ashruba Nanware. (2021). Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative. Pure and Applied Mathematics Journal, 10(2), 38-48. https://doi.org/10.11648/j.pamj.20211002.11

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ACS Style

Jagdish Ashruba Nanware. Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative. Pure Appl. Math. J. 2021, 10(2), 38-48. doi: 10.11648/j.pamj.20211002.11

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AMA Style

Jagdish Ashruba Nanware. Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative. Pure Appl Math J. 2021;10(2):38-48. doi: 10.11648/j.pamj.20211002.11

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@article{10.11648/j.pamj.20211002.11,
  author = {Jagdish Ashruba Nanware},
  title = {Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {2},
  pages = {38-48},
  doi = {10.11648/j.pamj.20211002.11},
  url = {https://doi.org/10.11648/j.pamj.20211002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211002.11},
  abstract = {In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.},
 year = {2021}
}

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TY  - JOUR
T1  - Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative
AU  - Jagdish Ashruba Nanware
Y1  - 2021/03/26
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211002.11
DO  - 10.11648/j.pamj.20211002.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 38
EP  - 48
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211002.11
AB  - In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.
VL  - 10
IS  - 2
ER  -

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Author Information

Jagdish Ashruba Nanware

Department of Mathematics, Shrikrishna College, Gunjoti, India

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Jagdish Ashruba Nanware. (2021). Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative. Pure and Applied Mathematics Journal, 10(2), 38-48. https://doi.org/10.11648/j.pamj.20211002.11

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ACS Style

Jagdish Ashruba Nanware. Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative. Pure Appl. Math. J. 2021, 10(2), 38-48. doi: 10.11648/j.pamj.20211002.11

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AMA Style

Jagdish Ashruba Nanware. Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative. Pure Appl Math J. 2021;10(2):38-48. doi: 10.11648/j.pamj.20211002.11

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@article{10.11648/j.pamj.20211002.11,
  author = {Jagdish Ashruba Nanware},
  title = {Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative},
  journal = {Pure and Applied Mathematics Journal},
  volume = {10},
  number = {2},
  pages = {38-48},
  doi = {10.11648/j.pamj.20211002.11},
  url = {https://doi.org/10.11648/j.pamj.20211002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20211002.11},
  abstract = {In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Qualitative Properties of Solutions of Finite System of Differential Equations Involving R-L Sequential Fractional Derivative
AU  - Jagdish Ashruba Nanware
Y1  - 2021/03/26
PY  - 2021
N1  - https://doi.org/10.11648/j.pamj.20211002.11
DO  - 10.11648/j.pamj.20211002.11
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 38
EP  - 48
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20211002.11
AB  - In this paper, qualitative properties such as existence-uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative with initial conditions have been studied. Lower and upper solutions are defined for the problem under investigation. Comparison results are used to develop monotone technique for finite system of differential equations involving R-L sequential fractional derivative with initial conditions when the functions on the right hand side are mixed quasi-monotone. Two convergent monotone sequences are obtained by introducing monotone operator. Lipschitz condition is the key part of the study. Minimal and maximal solutions are obtained by using developed technique. Existence and uniqueness of solutions of finite system of differential equations involving R-L sequential fractional derivative is also proved as an application of the technique.
VL  - 10
IS  - 2
ER  -

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