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Singh, Deepak, Verma, Sag. (1405). A study of a fractal multi-pantograph delay model with varying coefficients using fractional order wavelets. سامانه مدیریت نشریات علمی, 14(2), 828-851. doi: 10.22034/cmde.2025.62311.2735
Deepak Singh; Sag Ram Verma. "A study of a fractal multi-pantograph delay model with varying coefficients using fractional order wavelets". سامانه مدیریت نشریات علمی, 14, 2, 1405, 828-851. doi: 10.22034/cmde.2025.62311.2735
Singh, Deepak, Verma, Sag. (1405). 'A study of a fractal multi-pantograph delay model with varying coefficients using fractional order wavelets', سامانه مدیریت نشریات علمی, 14(2), pp. 828-851. doi: 10.22034/cmde.2025.62311.2735
Singh, Deepak, Verma, Sag. A study of a fractal multi-pantograph delay model with varying coefficients using fractional order wavelets. سامانه مدیریت نشریات علمی, 1405; 14(2): 828-851. doi: 10.22034/cmde.2025.62311.2735

A study of a fractal multi-pantograph delay model with varying coefficients using fractional order wavelets

Computational Methods for Differential Equations
مقاله 21، دوره 14، شماره 2، تیر 2026، صفحه 828-851    اصل مقاله (3.21 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.62311.2735
نویسندگان
Deepak Singh؛ Sag Ram Verma*
Department of Mathematics and Statistics, Gurukula Kangari (Deemed to be University), Haridwar, 249404, Uttarakhand, India.
چکیده
Apart from using fractal dimensions to describe statistical self-similarity, exploring a direct measurement approach involves considering mathematical models capable of constructing a real-world fractal entity, as classical differential and integral operators cannot efficiently handle such problems. In this study, the fractal derivative is applied to develop a fractal model for multi-pantograph delay differential equations with variable coefficients. The wavelet approach, employing Jacobi fractional order wavelets, has been developed to attain a numerical solution. The proposed methodology relies on the utilization of the fractal integral operational matrix of Jacobi fractional-order wavelets combined with the collocation method. We have outlined pseudo-code and conducted a stability analysis for the methods proposed within the specified model. Furthermore, the convergence analysis of the approximate solution is presented through some lemmas and theorems. The numerical results and error analysis of some illustrative examples are also shown in the tables and graphs. In the proposed methods, numerical results are derived across various values of the fractal $(\mu)$ and fractional $(\phi)$ parameters. It is important to highlight that the classical scenario is retrieved when $\mu=1$.
کلیدواژه‌ها
Fractal operator؛ Multi-pantograph delay differential equation؛ Fractional order Jacobi wavelets؛ Function approximation؛ Integral operational matrix
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تعداد مشاهده مقاله: 239
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