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Yadav LK, Agarwal G, Suthar DL, Purohit SD. Time-fractional partial differential equations: a novel technique for analytical and numerical solutions. ARAB JOURNAL OF BASIC AND APPLIED SCIENCES 2022. [DOI: 10.1080/25765299.2022.2064075] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022] Open
Affiliation(s)
- Lokesh Kumar Yadav
- Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, India
| | - Garima Agarwal
- Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, India
| | - D. L. Suthar
- Department of Mathematics, Wollo University, Dessie, Ethiopia
| | - S. D. Purohit
- Department of HEAS (Mathematics), Rajasthan Technical University, Kota, India
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Natural Transform Decomposition Method for Solving Fractional-Order Partial Differential Equations with Proportional Delay. MATHEMATICS 2019. [DOI: 10.3390/math7060532] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In the present article, fractional-order partial differential equations with proportional delay, including generalized Burger equations with proportional delay are solved by using Natural transform decomposition method. Natural transform decomposition method solutions for both fractional and integer orders are obtained in series form, showing higher convergence of the proposed method. Illustrative examples are considered to confirm the validity of the present method. Therefore, Natural transform decomposition method is considered to be one of the best analytical technique, to solve fractional-order linear and non-linear Partial deferential equations particularly fractional-order partial differential equations with proportional delay.
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Singh BK, Gupta M. A comparative study of analytical solutions of space-time fractional hyperbolic-like equations with two reliable methods. ARAB JOURNAL OF BASIC AND APPLIED SCIENCES 2019. [DOI: 10.1080/25765299.2018.1538067] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022] Open
Affiliation(s)
- Brajesh Kumar Singh
- Department of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, India
| | - Mukesh Gupta
- Department of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, India
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Singh BK, Kumar P. Extended Fractional Reduced Differential Transform for Solving Fractional Partial Differential Equations with Proportional Delay. INTERNATIONAL JOURNAL OF APPLIED AND COMPUTATIONAL MATHEMATICS 2017; 3:631-649. [DOI: 10.1007/s40819-017-0374-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/25/2023]
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