Generalized operational matrices to analyze inhomogeneous multi-term fractional differential equations : An efficient direct method
*Srimanti RoychoudhuryCorresponding authorsrimanti.eee@diu.edu.bdDepartment of Electrical and Electronic EngineeringDaffodil International UniversityDhaka, 1216, Bangladesh0000-0003-4611-1665View full profile → , Ubaidur Rahmanubaidur.eee@gmal.comDepartment of Electrical and Electronic EngineeringDaffodil International UniversityDhaka, 1216, Bangladesh0009-0004-6125-1142View full profile → , Afaque Wajidafaquewajid@gmail.comDepartment of Engineering Research and DesignTata Technologies LtdBangalore, Karnataka, 560103, India0000-0002-7580-3831View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Oct 2023
- Published Online:
- 15 Jul 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1602
- Pages:
- 951–976
Abstract
Keywords
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References
[1] T. Mahmood, M. ur Rahman, M. Arfan, S. I. Kayani, and M. Sun, Mathematical study of Algae as a bio-fertilizer using fractal–fractional dynamic model, Mathematics and Computers in Simulation, vol. 203, pp. 207-222 (2023).
[2] B. Abdullaeva, M. J. C. Opulencia, V. Borisov, K. F. Uktamov, W. K. Abdelbasset, A. K. J. Al-Nussair, and A. H. Jabbar, Optimal variable estimation of a Li-ion battery model by fractional calculus and bio-inspired algorithms, Journal of Energy Storage, vol. 54, 105323 (2022).
[3] H. P. Ren, X. Wang, J. T. Fan, and O. Kaynak, Fractional order sliding mode control of a pneumatic position servo system, Journal of the Franklin Institute, vol. 356, no. 12, pp. 6160-6174 (2019).
[4] L. Liu, L. Zhang, G. Pan, and S. Zhang, Robust yaw control of autonomous underwater vehicle based on fractional-order PID controller, Ocean Engineering, vol. 257, 111493 (2022).
[5] K. Vanchinathan, and N. Selvaganesan, Adaptive fractional order PID controller tuning for brushless DC motor using artificial bee colony algorithm, Results in Control and Optimization, vol. 4, 100032 (2021).
[6] B. Hekimoğlu, Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm, IEEE Access, vol. 7, pp. 38100-38114 (2019).
[7] S. Roychoudhury, U. Rahman and Md. S. H. Rabbi, Estimating Response of Fractional Order Systems and Control: An Orthogonal HF-Based Approach, International Conference on Signal Processing, Information, Communication and Systems 2024 (SPICSCON-2024), IEEE, Khulna, Bangladesh (2024).
[8] H. Almusawa, and A. Jhangeer, A study of the soliton solutions with an intrinsic fractional discrete nonlinear electrical transmission line, Fractal and Fractional, vol. 6, no. 6, pp. 334 (2022).
[9] H. Almusawa, A. Jhangeer, and M. Munawar, M., Analytical analyses for a fractional low-pass electrical transmission line model with dynamic transition. Symmetry, vol. 14, no. 7, pp. 1377 (2022).
[10] J. P. Hollkamp, and F. Semperlotti, Application of fractional order operators to the simulation of ducts with acoustic black hole terminations, Journal of Sound and Vibration, vol. 465, pp. 115035 (2020).
[11] K. S. Mawonou, A. Eddahech, D. Dumur, D. Beauvois, D., and E. Godoy, Improved state of charge estimation for Li-ion batteries using fractional order extended Kalman filter, Journal of Power Sources, vol. 435, pp. 226710 (2019).
[12] J. I. Hidalgo-Reyes, J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, V. M. Alvarado-Martínez, and M. G. López-López, Classical and fractional-order modeling of equivalent electrical circuits for supercapacitors and batteries, energy management strategies for hybrid systems and methods for the state of charge estimation: A state of the art review, Microelectronics Journal, vol. 85, pp. 109-128 (2019).
[13] K. S. Mawonou, A. Eddahech, D. Dumur, D. Beauvois, and E. Godoy, Improved state of charge estimation for Li-ion batteries using fractional order extended Kalman filter, Journal of Power Sources, vol. 435, pp. 226710 (2019).
[14] X. Wu, and Y. Huang, Adaptive fractional-order non-singular terminal sliding mode control based on fuzzy wavelet neural networks for omnidirectional mobile robot manipulator, ISA transactions, vol. 121, pp. 258-267 (2022).
[15] M. I. Haro-Olmo, I. Tejado, B. M. Vinagre, and V. Feliu-Batlle, Fractional-Order Models of Damping Phenomena in a Flexible Sensing Antenna Used for Haptic Robot Navigation, Fractal and Fractional, vol. 7, no. 8, pp. 621 (2023).
[16] S. Roychoudhury, A. Deb, and G. Sarkar, Analysis and synthesis of time-varying systems via orthogonal hybrid functions (HF) in state space environment, International Journal of Dynamics and Control, vol. 3, pp. 389-402 (2015).
[17] S. Roychoudhury, and A. Deb, Identification of multi-delay systems using orthogonal hybrid functions in state space environment, International Journal of Modelling, Identification and Control, vol. 30, no. 2, pp. 93-104 (2018).
[18] T. F. Nonnenmacher, and R. Metzler, On the Riemann-Liouville fractional calculus and some recent applications, Fractals, vol. 3, no. 3, pp. 557-566 (1995).
[19] T. Abdeljawad, On Riemann and Caputo fractional differences, Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1602-1611 (2011).
[20] M. D. Ortigueira, L. Rodríguez-Germá, and J. J. Trujillo, Complex Grünwald–Letnikov, Liouville, Riemann–Liouville, and Caputo derivatives for analytic functions, Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4174-4182 (2011).
[21] S. Roychoudhury, A. Deb, and G. Sarkar, Analysis and synthesis of homogeneous/non-homogeneous control systems via orthogonal hybrid functions (HF) under state space environment, Journal of Information and Optimization Sciences, vol. 35, no. 5-6, pp. 431-482 (2014).
[22] J. F. Neville, and A. C. Joseph, Systems-based decomposition schemes for the approximate solution of multi-term fractional differential equations, Journal of Computational and Applied mathematics, vol. 229, pp. 382-391 (2009).
[23] S. C. Shiralashetti and A. B. Deshi, An efficient Haar Wavelet collocation method for the numerical solution of multi-term fractional differential equations, Nonlinear Dyn, vol. 83, pp. 293-303 (2016).




