Fractional-Order Variational Calculus with Generalized Boundary Conditions [PDF]
Advances in Difference Equations, 2011 تقدم هذه الورقة شروط الأمثلية الضرورية والكافية للمشاكل المتغيرة الكسرية التي تنطوي على التكاملات الكسرية اليمنى واليسرى والمشتقات الكسرية المحددة بمعنى ريمان- ليوفيل مع لاغرانج اعتمادًا على نقاط النهاية الحرة. لتوضيح نهجنا، نناقش مثالين بالتفصيل.
Mohamed A. E. Herzallah +1 more
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Review of Some Promising Fractional Physical Models [PDF]
, 2015 Fractional dynamics is a field of study in physics and mechanics investigating the behavior of objects and systems that are characterized by power-law non-locality, power-law long-term memory or fractal properties by using integrations and ...
Tarasov, Vasily E.
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Generalized Memory: Fractional Calculus Approach [PDF]
Fractal and Fractional, 2018 The memory means an existence of output (response, endogenous variable) at the present time that depends on the history of the change of the input (impact, exogenous variable) on a finite (or infinite) time interval. The memory can be described by the function that is called the memory function, which is a kernel of the integro-differential operator ...
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Fractional calculus of variations with a generalized fractional derivative [PDF]
Fractional Differential Calculus, 2016 Summary: In this paper, we introduce a generalization of the Hilfer-Prabhakar derivative and obtain the Euler-Lagrange equations and Hamiltonian formulation with respect to this fractional derivative in the theory of fractional calculus of variations. Also, we get a sufficient condition for optimality.
Askari, Hassan, Ansari, Alireza
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Discrete Mittag-Leffler Functions in Linear Fractional Difference Equations
Abstract and Applied Analysis, 2011 This paper investigates some initial value problems in discrete fractional calculus. We introduce a linear difference equation of fractional order along with suitable initial conditions of fractional type and prove the existence and uniqueness of the ...
Jan Čermák +2 more
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Fractional conservation laws in optimal control theory
, 2007 Using the recent formulation of Noether's theorem for the problems of the calculus of variations with fractional derivatives, the Lagrange multiplier technique, and the fractional Euler-Lagrange equations, we prove a Noether-like theorem to the more ...
D. Baleanu +30 more
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A comparison between numerical solutions to fractional differential equations: Adams-type predictor-corrector and multi-step generalized differential transform method [PDF]
, 2017 In this note, two numerical methods of solving fractional differential equations (FDEs) are briefly described, namely predictor-corrector approach of Adams-Bashforth-Moulton type and multi-step generalized differential transform method (MSGDTM), and then
Ahrabi, Sima Sarv, Momenzadeh, Alireza
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A Generalized Fractional Calculus of Variations
, 2013 This is a preprint of a paper whose final and definitive form will appear in Control and Cybernetics.
Odzijewicz, T. +2 more
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Analysis of the family of integral equation involving incomplete types of I and Ī-functions
Applied Mathematics in Science and Engineering, 2023 The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete $ \bar {I} $ -function (I $ \bar {I} $ F) in its kernel.
Sanjay Bhatter +5 more
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Special Functions of Fractional Calculus in the Form of Convolution Series and Their Applications
Mathematics, 2021 In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero.
Yuri Luchko
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