Results 41 to 50 of about 2,487 (168)
, 2018 Here, the concept of a new and interesting Riemann–Liouville type fractional derivative operator is exploited. Treatment of a fractional derivative operator has been made associated with the extended Appell hypergeometric functions of two variables and ...
M. Faisal Khan +2 more
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Composition of Fractional Integral and Derivative Operators: Summarised in Tables
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT This paper compiles a complete, detailed list of composition properties for Riemann–Liouville fractional differintegrals, in all possible cases for orders anywhere in the complex plane, with the results presented clearly in a table for easy visual consumption.
Arran Fernandez
wiley +1 more source
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We develop a unified mathematical framework extending classical moment theory from discrete integer orders to a continuous spectrum of real orders f>0$$ f>0 $$, providing a systematic statistical characterization of complex systems exhibiting power‐law behavior.
Farrukh A. Chishtie
wiley +1 more source
Cauchy problems for fractional differential equations with Riemann–Liouville fractional derivatives
Journal of Functional Analysis, 2012 In this paper, the authors study certain Cauchy-type problems of fractional differential equations with fractional differential conditions, involving Riemann-Liouville derivatives, in infinite-dimensional Banach spaces. They introduce a certain fractional resolvent and study some of its properties.
Li, Kexue, Peng, Jigen, Jia, Junxiong
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Fractional boundary value problems with Riemann-Liouville fractional derivatives [PDF]
Advances in Difference Equations, 2015 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tan, Jingjing, Cheng, Caozong
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On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
wiley +1 more source
Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces [PDF]
, 2022 We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by Ws,1(a,b), and the fractional bounded variation spaces of fractional ...
Antonio Leaci +3 more
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Fractional Telegraph equation with the Riemann-Liouville derivative
, 2023 The Telegraph equation $(\partial_{t}^{ρ})^{2}u(x,t)+2α\partial_{t}^{ρ}u(x,t)-u_{xx}(x,t)=f(x,t)$, where ...
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Fractional Cauchy Problem with Riemann-Liouville Fractional Delta Derivative on Time Scales [PDF]
Abstract and Applied Analysis, 2013 Summary: The \(\Delta\)-power function and fractional \(\Delta\)-integrals and fractional \(\Delta\)-differential are defined, and then the definitions and properties of \(\Delta\)-Mittag-Leffler function are given. The properties of fractional \(\Delta\)-integrals and fractional \(\Delta\)-differential on time scales are discussed in detail.
Jiang Zhu, Ying Zhu
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Sliding Mode Control in Aerospace Applications: A Survey
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Sliding mode control (SMC) enjoys robustness to matched and unmatched (in the case of minimum phase input‐output dynamics) bounded perturbations, and finite time convergence. Second‐order and higher‐order sliding mode control systems (2‐SMC/HOSMC) retain all the advantages of sliding mode control, but in addition can be applied to systems of ...
Yuri Shtessel, Christopher Edwards
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