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پایگاه استنادی علوم جهان اسلام (ISC)

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Valizadeh, Moslem, Mahmoudi, Yaghoub, Dastmalchi Saei, Farhad. (1403). On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation. سامانه مدیریت نشریات علمی, 12(3), 511-522. doi: 10.22034/cmde.2023.58018.2444
Moslem Valizadeh; Yaghoub Mahmoudi; Farhad Dastmalchi Saei. "On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation". سامانه مدیریت نشریات علمی, 12, 3, 1403, 511-522. doi: 10.22034/cmde.2023.58018.2444
Valizadeh, Moslem, Mahmoudi, Yaghoub, Dastmalchi Saei, Farhad. (1403). 'On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation', سامانه مدیریت نشریات علمی, 12(3), pp. 511-522. doi: 10.22034/cmde.2023.58018.2444
Valizadeh, Moslem, Mahmoudi, Yaghoub, Dastmalchi Saei, Farhad. On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation. سامانه مدیریت نشریات علمی, 1403; 12(3): 511-522. doi: 10.22034/cmde.2023.58018.2444

On fractional linear multi-step methods for fractional order multi-delay nonlinear pantograph equation

Computational Methods for Differential Equations
مقاله 7، دوره 12، شماره 3، مهر 2024، صفحه 511-522    اصل مقاله (585.19 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.58018.2444
نویسندگان
Moslem Valizadeh؛ Yaghoub Mahmoudi* ؛ Farhad Dastmalchi Saei
Mathematics Department, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
چکیده
This paper presents the development of a series of fractional multi-step linear finite difference methods (FLMMs) designed to address fractional multi-delay pantograph differential equations of order $0 < \alpha \leq 1$. These $p$ FLMMs are constructed using fractional backward differentiation formulas of first and second orders, thereby facilitating the numerical solution of fractional differential equations. Notably, we employ accurate approximations for the delayed components of the equation, guaranteeing the retention of stability and convergence characteristics in the proposed $p$-FLMMs. To substantiate our theoretical findings, we offer numerical examples that corroborate the efficacy and reliability of our approach.
کلیدواژه‌ها
Fractional derivative؛ Fractional integration؛ Fractional linear multi-step methods
مراجع
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