Results 61 to 70 of about 5,231 (286)
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6425-6446, April 2025.ABSTRACT The well‐posedness results for mild solutions to the fractional neutral stochastic differential system with Rosenblatt process with Hurst index Ĥ∈12,1$$ \hat{H}\in \left(\frac{1}{2},1\right) $$ is discussed in this article. To demonstrate the results, the concept of bounded integral contractors is combined with the stochastic result and ...
Dimplekumar N. Chalishajar +3 more
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Riemann and Riemann-type Integration in Banach Spaces
Real Analysis Exchange, 2014 Riemann, Riemann-Dunford, Riemann-Pettis and Darboux integrable functions with values in a Banach space and Riemann-Gelfand integrable functions with values in the dual of a Banach space are studied in the light of the work of Graves, Alexiewicz and Orlicz, and Gordon.
Ali, Sk. Jaker, Mondal, Pratikshan
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Equivalences of Nonlinear Higher Order Fractional Differential Equations With Integral Equations
Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6930-6942, April 2025.ABSTRACT Equivalences of initial value problems (IVPs) of both nonlinear higher order (Riemann–Liouville type) fractional differential equations (FDEs) and Caputo FDEs with the corresponding integral equations are studied in this paper. It is proved that the nonlinearities in the FDEs can be L1$$ {L}^1 $$‐Carathéodory with suitable conditions.
Kunquan Lan
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On Riemann Integral Quasicontinuity
Real Analysis Exchange, 2006 A function $f:\mathR ^n \to \mathR$ satisfies condition $(Q_{r,i}(x))$ (resp. ($Q_{r,s}(x))$, [$Q_{r,o}(x)$]) at a point $x$ if for each real $r > 0$ and for each set $U$ containing $x$ and belonging to Euclidean topology in $\mathR ^n$ (resp. to the strong density topology [to the ordinary density topology]) there is a regular domain $I$ such that ...
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The Existence of Moving Spike Patterns in an Attractive Chemotaxis Model
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We prove rigorously the existence of moving spike patterns in an attractive chemotaxis model with small diffusion coefficient for the chemical. In the zero diffusion limit, ϵ→0$$ \epsilon \to 0 $$, we prove that the non‐monotone traveling wave solutions of the system with ϵ>0$$ \epsilon >0 $$ converge to those of the system with ϵ=0$$ \epsilon
Tong Li, Casey Stone
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A Generalization of the Riemann-Lebesgue Theorem for Riemann Integrability
Real Analysis Exchange, 2020 A classical theorem of Riemann and Lebesgue says that a bounded function defined on a compact interval is Riemann integrable if and only if it is continuous almost everywhere. In this note, we generalize their result and show that the difference between the upper and lower Riemann integrals of a not necessarily Riemann integrable function equals the ...
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Exact analytical solutions of the Bloch equation for the hyperbolic‐secant and chirp pulses
Magnetic Resonance in Medicine, EarlyView.Abstract Purpose To improve the accuracy and generality of analytical solutions of the Bloch equation for the hyperbolic‐secant (HS1) and chirp pulses in order to facilitate application to truncated and composite pulses and use in quantitative methods.
Ryan H. B. Smith +2 more
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On spectral question of the Cauchy-Riemann operator with homogeneous boundary value conditions
Қарағанды университетінің хабаршысы. Математика сериясы, 2018 In this paper we consider the eigenvalue problem for the Cauchy - Riemann operator with homogeneous Dirichlet type boundary conditions. The statement of the problem is justified to the theorem of M. Otelbaev and A.N.
N.S. Imanbaev, B.E. Kanguzhin
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Optimal Control Applications and Methods, EarlyView.Hybrid Algorithm‐Based Optimal FOPI Controller in Three‐phase UPQC system ABSTRACT Time delay (TD) is a common phenomenon in practical systems. Most studies have focused on the classical notion of integer‐order TD. However, it should not be neglected that the delay can also be noninteger.
Erdinç Şahin
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Fractional Calculus for Non-Discrete Signed Measures
MathematicsIn this paper, we suggest a first-ever construction of fractional integral and differential operators based on signed measures including a vector-valued case. The study focuses on constructing the fractional power of the Riemann–Stieltjes integral with a
Vassili N. Kolokoltsov +1 more
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