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Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method

Yıl 2023, Sayı: 45, 18 - 29, 31.12.2023

Sevil Çulha Ünal

https://doi.org/10.53570/jnt.1344706

Öz

One of the prominent nonlinear partial differential equations in mathematical physics is the Clannish Random Walker’s Parabolic (CRWP) equation. This study uses Residual Power Series Method (RPSM) to solve the time fractional CRWP equation. In this equation, the fractional derivatives are considered in Caputo’s sense. The effectiveness of RPSM is illustrated with graphical results. The series solutions are utilized to represent the approximate solutions. Besides, the approximate solutions found by the suggested method ensure good accuracy when compared with the exact solution. Moreover, RPSM efficiently analyzes complex problems that emerge in the related mathematical and scientific fields.

Anahtar Kelimeler

Fractional partial differential equation Caputo derivative Clannish Random Walker’s Parabolic equation residual power series method approximate solution

Kaynakça

  • Y. Uğurlu, D. Kaya, Analytic Method for Solitary Solutions of Some Partial Differential Equations, Physics Letters A 370 (3-4) (2007) 251–259.
  • Y. Uğurlu, İ. E. İnan, B. Kilic, Analytic Solutions of Some Partial Differential Equations by Using Homotopy Perturbation Equation, World Applied Sciences Journal 12 (11) (2011) 2135–2139.
  • B. Kiliç, Exact Solutions for Nonlinear Evolution Equations with Jacobi Elliptic Function Rational Expansion Method, World Applied Sciences Journal 23 (12) (2013) 81–88.
  • M. S. Khatun, M. F. Hoque, M. A. Rahman, Multisoliton Solutions, Completely Elastic Collisions and Non-elastic Fusion Phenomena of Two PDEs, Pramana-Journal of Physics 88 (2017) Article Number 86 9 pages.
  • B. Ahmad, J. J. Nieto, Existence of Solutions for Nonlocal Boundary Value Problems of Higher-order Nonlinear Fractional Differential Equations, Hindawi Abstract and Applied Analysis (2009) Article ID 494720 9 pages.
  • Y. Wang, S. Liang, Q. Wang, Existence Results for Fractional Differential Equations with Integral and Multi-point Boundary Conditions, Boundary Value Problems 2018 (4) (2018) 11 pages.
  • M. Şenol, A. Ata, Approximate Solution of Time-fractional KdV Equations by Residual Power Series Method, Journal of Balıkesir University Institute of Science and Technology 20 (1) (2018) 430–439.
  • G. Akram, M. Sadaf, M. Abbas, I. Zainab, S. R. Gillani, Efficient Techniques for Traveling Wave Solutions of Time-fractional Zakharov-Kuznetsov Equation, Mathematics and Computers in Simulation 193 (2022) 607–622.
  • M. M. A. Qurashi, Z. Korpinar, D. Baleanu, M. Inc, A New Iterative Algorithm on the Time-fractional Fisher Equation: Residual Power Series Method, Advances in Mechanical Engineering 9 (9) (2017) 8 pages.
  • Z. Körpınar, The Residual Power Series Method for Solving Fractional Klein-Gordon Equation, Sakarya University Journal of Science 21 (3) (2017) 285–293.
  • M. N. Alam, I. Talib, B. Bazighifan, D. N. Chalishajar, B. Almarri, An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena, Mathematics 9 (8) (2021) 801 10 pages.
  • O. Guner, A. Bekir, Ö. Ünsal, Two Reliable Methods for Solving the Time Fractional Clannish Random Walker’s Parabolic Equation, Optik 127 (20) (2016) 9571–9577.
  • A. A. Al-Shawba, F. A. Abdullah, A. Azmi, M. A. Akbar, An Extension of Double (G'⁄G,1/G)-expansion Method for Conformable Fractional Differential Equations, Hindawi Complexity (2020) Article ID 7967328 13 pages.
  • H. Bulut, B. Kılıç, Exact Solutions for Some Fractional Nonlinear Partial Differential Equations via Kudryashov Method, Physical Sciences 8 (11) (2013) 24–31.
  • S. Ampun, S. Sungnul, S. Koonprasert, New Exact Solutions for the Time fractional Clannish Random Walker’s Parabolic Equation by the Improved (tan(Φ(ξ)/2))-expansion Method, in: C, Likasiri, T. Muakthonglang, P. Phetpradab, T. Suksamran, P. Rojanakul, K. Sangkhanan (Eds.), The 22nd Annual Meeting in Mathematics, Thailand, 2017, 13 pages.
  • E. Atilgan, O. Taşbozan, A. Kurt, S. T. Mohyud-Din, Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic (CRWP) Equation and Modified Benjamin-Bona-Mahony (BBM) Equation, Universal Journal of Mathematics and Applications 3 (2) (2020) 61–68.
  • A. Korkmaz, Explicit Exact Solutions to Some One-Dimensional Conformable Time Fractional Equations, Waves in Random and Complex Media 29 (1) (2019) 124–137.
  • D. Kumar, S. C. Ray, Application of Extended Exp(-φ(ξ))-expansion Method to the Nonlinear Conformable Time-fractional Partial Differential Equations, International Journal of Physical Research 7 (2) (2019) 81–93.
  • A. R. Seadawy, A. Ali, M. H. Raddadi, Exact and Solitary Wave Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic and Ablowitz-Kaup-Newell-Segur Equations via Modified Mathematical Methods, Results in Physics 26 (2021) Article ID 104374 10 pages.
  • I. Siddique, K. B. Mehdi, M. A. Akbar, H. A. E-W. Khalifa, A. Zafar, Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques, Hindawi Journal of Function Spaces 2022 (2022) Article ID 1680560 10 pages.
  • P. Wang, W. Shan, Y. Wang, Q. Li, Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of the Time Fractional Clannish Random Walker’s Parabolic Equation, Modern Physics Letters B 35 (4) (2021) 2150074 16 pages.
  • A. Almuneef, A. E. Hagag, Approximate Solution of the Fractional Differential Equation via the Natural Decomposition Method, Revista Internacional de Métodos Numércos para Cálculo y Diseño en Ingeniería 39 (4) (2023) 15 pages.
  • O. Taki-Eddine, B. Abdefatah, A Priori Estimates for Weak Solution for a Time-fractional Nonlinear Reaction-diffusion Equations with an Integral Condition, Chaos, Solitons & Fractals 103 (2017) 79–89.
  • M. Odabaşı, E. Mısırlı, On the solutions of the Nonlinear Fractional Differential Equations via the Modified Trial Equation Method, Mathematical Methods in the Applied Sciences 41 (2018) 904–911.
  • A. Arqub, Series Solution of Fuzzy Differential Equations Under Strongly Generalized Differentiability, Journal of Advanced Research in Applied Mathematics 5 (1) (2013) 31–52.
  • A. El-Ajou, O. A. Arqub, S. Momani, Approximate Analytical Solution of the Nonlinear Fractional KdV-Burgers Equation: A New Iterative Algorithm, Journal of Computational Physics 293 (2015) 81–95.
  • M. Şenol, M. Alquran, H. D. Kasmaei, On the Comparison of Perturbation-iteration Algorithm and Residual Power Series Method to Solve Fractional Zakharov-Kuznetsov Equation, Results in Physics 9 (2018) 321–327.
  • S. Kumar, A. Kumar, D. Baleanu, Two Analytical Methods for Time-fractional Nonlinear Coupled Boussinesq-Burger’s Equations Arise in Propagation of Shallow Water Waves, Nonlinear Dynamics 85 (2016) 699–715.
  • M. Alquran, Analytical Solutions of Fractional Foam Drainage Equation by Residual Power Series Method, Mathematical Sciences 8 (2014) 153–160.
  • D. G. Prakasha, P. Veeresha, H. M. Baskonus, Residual Power Series Method for Fractional Swift-Hohenberg Equation, Fractal and Fractional 3 (1) (2019) 9 16 pages.
  • A. Kumar, S. Kumar, M. Singh, Residual Power Series Method for Fractional Sharma-Tasso-Olever Equation, Communications in Numerical Analysis 2016 (1) (2016) Article ID cna-00235 10 pages.
  • R. M. Jena, S. Chakraverty, Residual Power Series Method for Solving Time-fractional Model of Vibration Equation of Large Membranes, Journal of Applied and Computational Mechanics 5 (4) (2019) 603–615.
  • K. K. Jaber, R. S. Ahmad, Analytical Solution of the Time Fractional Navier-Stokes Equation, Ain Shams Engineering Journal 9 (4) (2018) 1917–1927.
  • A. Arafa, G. Elmahdy, Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow, Hindawi International Journal of Differential Equations, 2018 (2018) Article ID 7692849 10 pages.
  • M. H. Darassi, Y. A. Hour, Residual Power Series Technique for Solving Fokker-Planck Equation, Italian Journal of Pure and Applied Mathematics (44) (2020) 319–332.
  • M. Inc, Z. S. Korpinar, M. M. A. Qurashi, D. Baleanu, A New Method for Approximate Solutions of Some Nonlinear Equations: Residual Power Series Method, Advances in Mechanical Engineering 8 (4) (2016) 1–7.
  • H. M. Jaradat, S. Al-Shar’a, Q. J. A. Khan, M. Alquran, K. Al-Khaled, Analytical Solution of Time-fractional Drinfeld-Sokolov-Wilson System Using Residual Power Series Method, IAENG International Journal of Applied Mathematics 46 (1) (2016) 64–70.
  • Z. Korpinar, M. Inc, E. Hınçal, D. Baleanu, Residual Power Series Algorithm for Fractional Cancer Tumor Models, Alexandria Engineering Journal 59 (3) (2020) 1405–1412.
  • B. A. Mahmood, M. A. Yousif, A Residual Power Series Technique for Solving Boussinesq-Burgers Equations, Cogent Mathematics 4 (2017) Article ID 1279398 11 pages.
  • B. A. Mahmood, M. A. Yousif, A Novel Analytical Solution for the Modified Kawahara Equation Using the Residual Power Series Method, Nonlinear Dynamics 89 (2017) 1233–1238.
  • T. R. R. Rao, Application of Residual Power Series Method to Time Fractional Gas Dynamics Equations, in: S. Sivasankaran, S. Eswaramoorthi (Eds.), International Conference on Applied and Computational Mathematics, Tamilnadu, 2018, 5 pages.
  • H. Tariq, G. Akram, Residual Power Series Method for Solving Time-Space-Fractional Benney-Lin Equation Arising in Falling Film Problems, Journal of Applied Mathematics and Computing 55 (2017) 683–708.
  • H. Tariq, G. Akram, New Traveling Wave Exact and Approximate Solutions for the Nonlinear Cahn-Allen Equation: Evolution of a Nonconserved Quantity, Nonlinear Dynamics 88 (2017) 581–594.
  • F. Tchier, M. Inc, Z. S. Korpinar, D. Baleanu, Solutions of the Time Fractional Reaction-diffusion Equations with Residual Power Series Method, Advances in Mechanical Engineering 8 (10) (2016) 10 pages.
  • I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • A. El-Ajou, O. A. Arqub, Z. A. Zhour, S. Momani, New Results on Fractional Power Series: Theories and Applications, Entropy 15 (12) (2013) 5305–5323.
  • O. A. Arqub, Z. Abo-Hammour, R. Al-Badarneh, S. Momani, A Reliable Analytical Method for Solving Higher-Order Initial Value Problems, Hindawi Discrete Dynamics in Nature and Society (2013) Article ID 673829 12 pages.
  • O. A. Arqub, A. El-Ajou, Z. A. Zhour, S. Momani, Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique, Entropy 16 (2014) 471–493.
  • O. A. Arqub, A. El-Ajou, A. S. Bataineh, I. Hashim, A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method, Hindawi Abstract and Applied Analysis (2013) Article ID 378593 10 pages.

Yıl 2023, Sayı: 45, 18 - 29, 31.12.2023

Sevil Çulha Ünal

https://doi.org/10.53570/jnt.1344706

Öz

Kaynakça

  • Y. Uğurlu, D. Kaya, Analytic Method for Solitary Solutions of Some Partial Differential Equations, Physics Letters A 370 (3-4) (2007) 251–259.
  • Y. Uğurlu, İ. E. İnan, B. Kilic, Analytic Solutions of Some Partial Differential Equations by Using Homotopy Perturbation Equation, World Applied Sciences Journal 12 (11) (2011) 2135–2139.
  • B. Kiliç, Exact Solutions for Nonlinear Evolution Equations with Jacobi Elliptic Function Rational Expansion Method, World Applied Sciences Journal 23 (12) (2013) 81–88.
  • M. S. Khatun, M. F. Hoque, M. A. Rahman, Multisoliton Solutions, Completely Elastic Collisions and Non-elastic Fusion Phenomena of Two PDEs, Pramana-Journal of Physics 88 (2017) Article Number 86 9 pages.
  • B. Ahmad, J. J. Nieto, Existence of Solutions for Nonlocal Boundary Value Problems of Higher-order Nonlinear Fractional Differential Equations, Hindawi Abstract and Applied Analysis (2009) Article ID 494720 9 pages.
  • Y. Wang, S. Liang, Q. Wang, Existence Results for Fractional Differential Equations with Integral and Multi-point Boundary Conditions, Boundary Value Problems 2018 (4) (2018) 11 pages.
  • M. Şenol, A. Ata, Approximate Solution of Time-fractional KdV Equations by Residual Power Series Method, Journal of Balıkesir University Institute of Science and Technology 20 (1) (2018) 430–439.
  • G. Akram, M. Sadaf, M. Abbas, I. Zainab, S. R. Gillani, Efficient Techniques for Traveling Wave Solutions of Time-fractional Zakharov-Kuznetsov Equation, Mathematics and Computers in Simulation 193 (2022) 607–622.
  • M. M. A. Qurashi, Z. Korpinar, D. Baleanu, M. Inc, A New Iterative Algorithm on the Time-fractional Fisher Equation: Residual Power Series Method, Advances in Mechanical Engineering 9 (9) (2017) 8 pages.
  • Z. Körpınar, The Residual Power Series Method for Solving Fractional Klein-Gordon Equation, Sakarya University Journal of Science 21 (3) (2017) 285–293.
  • M. N. Alam, I. Talib, B. Bazighifan, D. N. Chalishajar, B. Almarri, An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena, Mathematics 9 (8) (2021) 801 10 pages.
  • O. Guner, A. Bekir, Ö. Ünsal, Two Reliable Methods for Solving the Time Fractional Clannish Random Walker’s Parabolic Equation, Optik 127 (20) (2016) 9571–9577.
  • A. A. Al-Shawba, F. A. Abdullah, A. Azmi, M. A. Akbar, An Extension of Double (G'⁄G,1/G)-expansion Method for Conformable Fractional Differential Equations, Hindawi Complexity (2020) Article ID 7967328 13 pages.
  • H. Bulut, B. Kılıç, Exact Solutions for Some Fractional Nonlinear Partial Differential Equations via Kudryashov Method, Physical Sciences 8 (11) (2013) 24–31.
  • S. Ampun, S. Sungnul, S. Koonprasert, New Exact Solutions for the Time fractional Clannish Random Walker’s Parabolic Equation by the Improved (tan(Φ(ξ)/2))-expansion Method, in: C, Likasiri, T. Muakthonglang, P. Phetpradab, T. Suksamran, P. Rojanakul, K. Sangkhanan (Eds.), The 22nd Annual Meeting in Mathematics, Thailand, 2017, 13 pages.
  • E. Atilgan, O. Taşbozan, A. Kurt, S. T. Mohyud-Din, Approximate Analytical Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic (CRWP) Equation and Modified Benjamin-Bona-Mahony (BBM) Equation, Universal Journal of Mathematics and Applications 3 (2) (2020) 61–68.
  • A. Korkmaz, Explicit Exact Solutions to Some One-Dimensional Conformable Time Fractional Equations, Waves in Random and Complex Media 29 (1) (2019) 124–137.
  • D. Kumar, S. C. Ray, Application of Extended Exp(-φ(ξ))-expansion Method to the Nonlinear Conformable Time-fractional Partial Differential Equations, International Journal of Physical Research 7 (2) (2019) 81–93.
  • A. R. Seadawy, A. Ali, M. H. Raddadi, Exact and Solitary Wave Solutions of Conformable Time Fractional Clannish Random Walker’s Parabolic and Ablowitz-Kaup-Newell-Segur Equations via Modified Mathematical Methods, Results in Physics 26 (2021) Article ID 104374 10 pages.
  • I. Siddique, K. B. Mehdi, M. A. Akbar, H. A. E-W. Khalifa, A. Zafar, Diverse Exact Soliton Solutions of the Time Fractional Clannish Random Walker’s Parabolic Equation via Dual Novel Techniques, Hindawi Journal of Function Spaces 2022 (2022) Article ID 1680560 10 pages.
  • P. Wang, W. Shan, Y. Wang, Q. Li, Lie Symmetry Analysis, Explicit Solutions and Conservation Laws of the Time Fractional Clannish Random Walker’s Parabolic Equation, Modern Physics Letters B 35 (4) (2021) 2150074 16 pages.
  • A. Almuneef, A. E. Hagag, Approximate Solution of the Fractional Differential Equation via the Natural Decomposition Method, Revista Internacional de Métodos Numércos para Cálculo y Diseño en Ingeniería 39 (4) (2023) 15 pages.
  • O. Taki-Eddine, B. Abdefatah, A Priori Estimates for Weak Solution for a Time-fractional Nonlinear Reaction-diffusion Equations with an Integral Condition, Chaos, Solitons & Fractals 103 (2017) 79–89.
  • M. Odabaşı, E. Mısırlı, On the solutions of the Nonlinear Fractional Differential Equations via the Modified Trial Equation Method, Mathematical Methods in the Applied Sciences 41 (2018) 904–911.
  • A. Arqub, Series Solution of Fuzzy Differential Equations Under Strongly Generalized Differentiability, Journal of Advanced Research in Applied Mathematics 5 (1) (2013) 31–52.
  • A. El-Ajou, O. A. Arqub, S. Momani, Approximate Analytical Solution of the Nonlinear Fractional KdV-Burgers Equation: A New Iterative Algorithm, Journal of Computational Physics 293 (2015) 81–95.
  • M. Şenol, M. Alquran, H. D. Kasmaei, On the Comparison of Perturbation-iteration Algorithm and Residual Power Series Method to Solve Fractional Zakharov-Kuznetsov Equation, Results in Physics 9 (2018) 321–327.
  • S. Kumar, A. Kumar, D. Baleanu, Two Analytical Methods for Time-fractional Nonlinear Coupled Boussinesq-Burger’s Equations Arise in Propagation of Shallow Water Waves, Nonlinear Dynamics 85 (2016) 699–715.
  • M. Alquran, Analytical Solutions of Fractional Foam Drainage Equation by Residual Power Series Method, Mathematical Sciences 8 (2014) 153–160.
  • D. G. Prakasha, P. Veeresha, H. M. Baskonus, Residual Power Series Method for Fractional Swift-Hohenberg Equation, Fractal and Fractional 3 (1) (2019) 9 16 pages.
  • A. Kumar, S. Kumar, M. Singh, Residual Power Series Method for Fractional Sharma-Tasso-Olever Equation, Communications in Numerical Analysis 2016 (1) (2016) Article ID cna-00235 10 pages.
  • R. M. Jena, S. Chakraverty, Residual Power Series Method for Solving Time-fractional Model of Vibration Equation of Large Membranes, Journal of Applied and Computational Mechanics 5 (4) (2019) 603–615.
  • K. K. Jaber, R. S. Ahmad, Analytical Solution of the Time Fractional Navier-Stokes Equation, Ain Shams Engineering Journal 9 (4) (2018) 1917–1927.
  • A. Arafa, G. Elmahdy, Application of Residual Power Series Method to Fractional Coupled Physical Equations Arising in Fluids Flow, Hindawi International Journal of Differential Equations, 2018 (2018) Article ID 7692849 10 pages.
  • M. H. Darassi, Y. A. Hour, Residual Power Series Technique for Solving Fokker-Planck Equation, Italian Journal of Pure and Applied Mathematics (44) (2020) 319–332.
  • M. Inc, Z. S. Korpinar, M. M. A. Qurashi, D. Baleanu, A New Method for Approximate Solutions of Some Nonlinear Equations: Residual Power Series Method, Advances in Mechanical Engineering 8 (4) (2016) 1–7.
  • H. M. Jaradat, S. Al-Shar’a, Q. J. A. Khan, M. Alquran, K. Al-Khaled, Analytical Solution of Time-fractional Drinfeld-Sokolov-Wilson System Using Residual Power Series Method, IAENG International Journal of Applied Mathematics 46 (1) (2016) 64–70.
  • Z. Korpinar, M. Inc, E. Hınçal, D. Baleanu, Residual Power Series Algorithm for Fractional Cancer Tumor Models, Alexandria Engineering Journal 59 (3) (2020) 1405–1412.
  • B. A. Mahmood, M. A. Yousif, A Residual Power Series Technique for Solving Boussinesq-Burgers Equations, Cogent Mathematics 4 (2017) Article ID 1279398 11 pages.
  • B. A. Mahmood, M. A. Yousif, A Novel Analytical Solution for the Modified Kawahara Equation Using the Residual Power Series Method, Nonlinear Dynamics 89 (2017) 1233–1238.
  • T. R. R. Rao, Application of Residual Power Series Method to Time Fractional Gas Dynamics Equations, in: S. Sivasankaran, S. Eswaramoorthi (Eds.), International Conference on Applied and Computational Mathematics, Tamilnadu, 2018, 5 pages.
  • H. Tariq, G. Akram, Residual Power Series Method for Solving Time-Space-Fractional Benney-Lin Equation Arising in Falling Film Problems, Journal of Applied Mathematics and Computing 55 (2017) 683–708.
  • H. Tariq, G. Akram, New Traveling Wave Exact and Approximate Solutions for the Nonlinear Cahn-Allen Equation: Evolution of a Nonconserved Quantity, Nonlinear Dynamics 88 (2017) 581–594.
  • F. Tchier, M. Inc, Z. S. Korpinar, D. Baleanu, Solutions of the Time Fractional Reaction-diffusion Equations with Residual Power Series Method, Advances in Mechanical Engineering 8 (10) (2016) 10 pages.
  • I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
  • A. El-Ajou, O. A. Arqub, Z. A. Zhour, S. Momani, New Results on Fractional Power Series: Theories and Applications, Entropy 15 (12) (2013) 5305–5323.
  • O. A. Arqub, Z. Abo-Hammour, R. Al-Badarneh, S. Momani, A Reliable Analytical Method for Solving Higher-Order Initial Value Problems, Hindawi Discrete Dynamics in Nature and Society (2013) Article ID 673829 12 pages.
  • O. A. Arqub, A. El-Ajou, Z. A. Zhour, S. Momani, Multiple Solutions of Nonlinear Boundary Value Problems of Fractional Order: A New Analytic Iterative Technique, Entropy 16 (2014) 471–493.
  • O. A. Arqub, A. El-Ajou, A. S. Bataineh, I. Hashim, A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method, Hindawi Abstract and Applied Analysis (2013) Article ID 378593 10 pages.
Toplam 49 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Araştırma Makalesi
Yazarlar

Sevil Çulha Ünal 0000-0001-7447-9219

Erken Görünüm Tarihi 30 Aralık 2023
Yayımlanma Tarihi 31 Aralık 2023
Gönderilme Tarihi 17 Ağustos 2023
Yayımlandığı Sayı Yıl 2023 Sayı: 45

Kaynak Göster

APA Çulha Ünal, S. (2023). Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method. Journal of New Theory(45), 18-29. https://doi.org/10.53570/jnt.1344706
AMA Çulha Ünal S. Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method. JNT. Aralık 2023;(45):18-29. doi:10.53570/jnt.1344706
Chicago Çulha Ünal, Sevil. “Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation With the Residual Power Series Method”. Journal of New Theory, sy. 45 (Aralık 2023): 18-29. https://doi.org/10.53570/jnt.1344706.
EndNote Çulha Ünal S (01 Aralık 2023) Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method. Journal of New Theory 45 18–29.
IEEE S. Çulha Ünal, “Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method”, JNT, sy. 45, ss. 18–29, Aralık 2023, doi: 10.53570/jnt.1344706.
ISNAD Çulha Ünal, Sevil. “Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation With the Residual Power Series Method”. Journal of New Theory 45 (Aralık 2023), 18-29. https://doi.org/10.53570/jnt.1344706.
JAMA Çulha Ünal S. Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method. JNT. 2023;:18–29.
MLA Çulha Ünal, Sevil. “Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation With the Residual Power Series Method”. Journal of New Theory, sy. 45, 2023, ss. 18-29, doi:10.53570/jnt.1344706.
Vancouver Çulha Ünal S. Approximate Solutions of the Fractional Clannish Random Walker’s Parabolic Equation with the Residual Power Series Method. JNT. 2023(45):18-29.
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