Volume 26 , Issue 3 , PP: 339-358, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Abdulsalam Al-Dulaimi 1 * , Amirah Azmi 2 , Yaseen S. R. 3
Doi: https://doi.org/10.54216/IJNS.260325
Applying Chebyshev polynomial approximate results, this paper applies the idea of neutrophilic logic to the approach to partially differential equations (FPDEs). Three elements make up the Neutrosophic technique: Indeterminacy (I), Falsehood (F), and Truth (T). These three elements are appropriate for issues where precise values or distinct limits are lacking since they are utilized to represent ambiguity, vagueness, and imperfect truth in mathematical models. We improve the depiction of real-world occurrences that could contain unclear or ambiguous information by adding these values to the coefficients of FPDEs. In domains like material science, mechanical engineering, and biological phenomena, where uncertainty is inevitable, the use of neutrophilic logic enables a more thorough and precise approximation of approaches to complicated fractional differential equations. The findings show that when working with systems that have unknown characteristics, the Neutrosophic technique increases the accuracy and dependability of computations.
Chebyshev Polynomial , Caputo derivatives , Neutrosophic applications , Fractional differential issues ,
[1] D. Bhatta and D. Debnath, "Small amplitude wave in shallow water over linear and quadratic sloping beds," Journal of Applied Mathematics and Computing, vol. 13, pp. 53-65, 2003.
[2] L. Debnath, "The Legacy of Leonhard Euler: A Tricentennial Tribute," International Journal of Mathematical Education in Science and Technology, vol. 40, pp. 353-388, 2009.
[3] V. Tarasov, "Vector calculus in non-integer dimensional space and its applications to fractal media," Communications in Nonlinear Science and Numerical Simulation, vol. 20, pp. 360-374, 2015.
[4] J. Tenreiro, A. Mainardi, and V. Kiryakova, "Fractional Calculus: Where are we Going?" Fractional Calculus and Applied Analysis, vol. 18, pp. 495-526, 2015.
[5] F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, London, UK: Imperial College Press, 2010, pp. 1-154.
[6] W. Abdul-Majid, "A reliable modification of Adomian decomposition method," Applied Mathematics and Computation, vol. 102, pp. 77-86, 1999.
[7] J. He, "Homotopy Perturbation Technique," Computer Methods in Applied Mechanics and Engineering, vol. 178, pp. 257-262, 1999.
[8] V. Gupta and G. Sumit, "Application of Homotopy Analysis Method for Solving Nonlinear Cauchy Problem," Surveys in Mathematics and its Applications, vol. 7, pp. 105-116, 2012.
[9] O. Zaid and M. Shaher, "The Variational Iteration Method: An Efficient Scheme for Handling Fractional Partial Differential Equations in Fluid Mechanics," Computers and Mathematics with Applications, vol. 58, pp. 2199-2208, 2009.
[10] G. Daftardar and H. Jafari, "Iterative Method for Solving Nonlinear Fractional Equations," Journal of Mathematical Analysis and Applied Sciences, vol. 316, pp. 753-763, 2006.
[11] R. Jiwari, S. Pandit, and R. Mittal, "A differential quadrature algorithm to solve the two-dimensional linear hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions," Applied Mathematics and Computation, vol. 218, pp. 7279-7294, 2012.
[12] W. Kangle and L. Sanyang, "A new Sumudu transform iterative for time-fractional Cauchy reaction-diffusion," vol. 5, pp. 1-865, 2016.
[13] D. Chandradeepa and R. Vasant, "Solution of fractional partial differential equations using iterative method," Fractional Calculus and Applied Analysis, vol. 15, pp. 684-699, 2012.
[14] A. Roozi, E. Alibeiki, S. Hossein, M. Shafiof, and M. Ebrahimi, "Homotopy perturbation method for special nonlinear partial differential equations," Journal of King Saud University, vol. 23, pp. 99-103, 2011.
[15] A. Kamel, "Numerical solution of time-fractional partial differential equations using Sumudu decomposition method," Romanian Journal of Physics, vol. 60, pp. 99-110, 2015.
[16] V. Galaktionov and S. Svirshchevskii, "Exact solutions and invariant subspaces of nonlinear partial differential equations in mechanics and physics," Chapman and Hall/CRC Applied Mathematics and Nonlinear Sciences Series, UK, 2007.
[17] A. Ouhadan and H. Elkinani, "Invariant subspace method and fractional modified Kuramoto-Sivashinsky equation," arXiv, pp. 1-12, 2015.
[18] S. Svirshchevskii, "Invariant linear spaces and exact solutions of nonlinear evolution equations," Journal of Nonlinear Mathematical Physics, vol. 3, pp. 164-169, 2013.
[19] R. Shadevan and T. Bakkyaraj, "Invariant subspace method and exact solutions of certain nonlinear time fractional partial differential equations," Fractional Calculus and Applied Analysis, vol. 18, pp. 146-162, 2015.
[20] R. Shadevan and P. Prakash, "Exact solution of certain time fractional nonlinear partial differential equations," Nonlinear Dynamics, vol. 85, pp. 659-673, 2016.
[21] S. Choudhary and G. Daftardar, "Invariant subspace method: A tool for solving fractional partial differential equations," Journal of Fractional Calculus and Applied Analysis, vol. 20, pp. 1-18, 2017.
[22] K. Zhukovsky, "Operational solution for some types of second order differential equations and for relevant physical problems," Journal of Mathematical Analysis and Applications, vol. 446, pp. 628-647, 2017.
[23] V. Gupta and B. Sharma, "Application of Sumudu transform in reaction-diffusion systems and nonlinear waves," Applied Mathematics Sciences (Ruse), 2010, pp. 1-10.
[24] F. Jarad, "Application of Sumudu and double Sumudu transforms to Caputo fractional differential equations," Journal of Computational Analysis and Applications, vol. 14, pp. 475-483, 2012.
[25] M. Tarig, M. Salih, and A. Elsayed, "On the new integral transform 'Elzaki transform': Fundamental properties investigation and applications," Global Journal of Mathematical Sciences: Theory and Practical, vol. 4, pp. 1-13, 2012.
[26] F. Smarandache, Neutrosophy: Neutrosophic Logic, Set, and Probability, American Research Press, 1995.
[27] B. H. Saleh and S. R. Yassen, "Several weak shapes in intuitionistic topological spaces," AIP Conference Proceedings, vol. 3264, pp. 1, AIP Publishing, 2025.
[28] R. A. Isewid, N. I. Aziz, S. R. Yaseen, and M. R. Qasem, "Some properties of regular and normal space on topological graph space," Journal of Physics: Conference Series, vol. 1879, pp. 022106, IOP Publishing, 2021.
[29] Q. H. Imran, A. H. M. Al-Obaidi, and F. Smarandache, "On Some Types of Neutrosophic Topological Groups with Respect to Neutrosophic Alpha Open Sets," Neutrosophic Sets and Systems, vol. 32, pp. 425-434, 2020.
[30] A. H. M. Al-Obaidi and Q. H. Imran, "On new types of weakly neutrosophic crisp open mappings," Iraqi Journal of Science, vol. 62, no. 8, pp. 2660-2666, 2021.
