Fractional Calculus and Applied Analysis最新文献_第4页

Abstract multi-term fractional difference equations 抽象多期分数差分方程

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-24 DOI: 10.1007/s13540-025-00391-8

Marko Kostić

引用次数: 0

Controllability of multi-term fractional-order impulsive dynamical systems with $$varphi $$ -Caputo fractional derivative 具有$$varphi $$ -Caputo分数阶导数的多项分数阶脉冲动力系统的可控性

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-24 DOI: 10.1007/s13540-025-00393-6

Md. Samshad Hussain Ansari, Muslim Malik

引用次数: 0

Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models 在分数阶自适应指数积分-火模型中模拟神经元动力学

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-24 DOI: 10.1007/s13540-025-00392-7

Alexandru Fikl, Aman Jhinga, Eva Kaslik, Argha Mondal

{"title":"Simulating neuronal dynamics in fractional adaptive exponential integrate-and-fire models","authors":"Alexandru Fikl, Aman Jhinga, Eva Kaslik, Argha Mondal","doi":"10.1007/s13540-025-00392-7","DOIUrl":"https://doi.org/10.1007/s13540-025-00392-7","url":null,"abstract":"We introduce an efficient discretisation of a novel fractional-order adaptive exponential (FrAdEx) integrate-and-fire model, which is used to study the fractional-order dynamics of neuronal activities. The discretisation is based on an extension of L1-type methods that can accurately handle exponential growth and the spiking mechanism of the model. This new method is implicit and uses adaptive time stepping to robustly handle the stiff system that arises due to the exponential term. The implicit nonlinear system can be solved exactly, without iterative methods, making the scheme efficient while maintaining accuracy. We present a complete error model for the numerical scheme that can be extended to other integrate-and-fire models with minor changes. To show the feasibility of our approach, the numerical method has been rigorously validated and used to investigate the diverse spiking oscillations of the model. We observed that the fractional-order model is capable of predicting biophysical activities, which are interpreted through phase diagrams describing the transition from one firing type to another. This simple model shows significant promise, as it has sufficient expressive dynamics to reproduce several features qualitatively from a biophysical dynamical perspective.","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143695524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Simple difference schemes for multidimensional fractional Laplacian and fractional gradient 多维分数阶拉普拉斯和分数阶梯度的简单差分格式

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-19 DOI: 10.1007/s13540-025-00386-5

Jaromír Kukal, Michal Beneš

引用次数: 0

Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators 与卡普托时间-分数阶导数和分数阶Schrödinger算子生成的半群相关的微分变换

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-17 DOI: 10.1007/s13540-025-00388-3

Zhiyong Wang, Pengtao Li, Yu Liu

{"title":"Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators","authors":"Zhiyong Wang, Pengtao Li, Yu Liu","doi":"10.1007/s13540-025-00388-3","DOIUrl":"https://doi.org/10.1007/s13540-025-00388-3","url":null,"abstract":"Let ({e^{-t{mathcal {L}}^{alpha }}}_{t>0}) be the heat semigroup related to the fractional Schrödinger operator (mathcal {L}^{alpha }:=(-varDelta +V)^{alpha }) with (alpha in (0,1)), where V is a non-negative potential belonging to the reverse Hölder class. In this paper, we analyze the convergence of the following type of the series $$begin{aligned} T_{N,t}^{alpha ,beta }(f)=sum _{j=N_{1}}^{N_{2}}v_{j}Big (t^{beta }partial _{t}^{beta }e^{-t{mathcal {L}}^{alpha }}(f)Big |_{t=t_{j+1}}- t^{beta }partial _{t}^{beta }e^{-t{mathcal {L}}^{alpha }}(f)Big |_{t=t_{j}}Big ) end{aligned}$$for (beta >0) and for any (N=(N_{1},N_{2})in mathbb {Z}^{2}) with (N_{1}<N_{2}), where ({t_{j}}_{jin mathbb {Z}}) is an increasing sequence in ((0,infty )) and ({v_{j}}_{jin mathbb {Z}}) is a bounded sequence of real numbers. The symbol (partial _{t}^{beta }) denotes the Caputo time-fractional derivative. We prove that the maximal operator (T_{*,t}^{alpha ,beta }(f)=sup _{begin{array}{c} Nin mathbb {Z}^{2} N_{1}<N_{2} end{array}}|T_{N,t}^{alpha ,beta }(f)|) is bounded on weighted Lebesgue spaces (L^{p}_{w}({mathbb {R}}^{n})), and is a bounded operator from (BMO_{{mathcal {L}},w}^{gamma }({mathbb {R}}^{n})) into (BLO_{{mathcal {L}},w}^{gamma }({mathbb {R}}^{n})), where (gamma in [0,1)) and w belongs to the class of weights associated with the auxiliary function (rho (x,V)).","PeriodicalId":48928,"journal":{"name":"Fractional Calculus and Applied Analysis","volume":"54 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2025-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143640438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis and computation for quenching solution to the time-space fractional Kawarada problem 时空分数型Kawarada问题淬火解的分析与计算

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-14 DOI: 10.1007/s13540-025-00384-7

Dingding Cao, Changpin Li

引用次数: 0

Investigation of controllability criteria for Caputo fractional dynamical systems with delays in both state and control 状态和控制均有时滞的Caputo分数阶动力系统的可控性准则研究

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-14 DOI: 10.1007/s13540-025-00387-4

Anjapuli Panneer Selvam, Venkatesan Govindaraj

引用次数: 0

On fractional derivatives of Djrbashian–Nersessian type with the nth-level Sonin kernels and their basic properties 具有n级Sonin核的djbashian - nersessian型的分数阶导数及其基本性质

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-14 DOI: 10.1007/s13540-025-00385-6

Mohammed Al-Refai, Yuri Luchko

引用次数: 0

Infinitely many solutions for impulsive fractional Schrödinger-Kirchhoff-type equations involving p-Laplacian via variational method 用变分方法求解脉冲分数阶Schrödinger-Kirchhoff-type方程的无穷多解

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-05 DOI: 10.1007/s13540-025-00380-x

Yi Wang, Lixin Tian

引用次数: 0

Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems 二维非自治Reissner-Mindlin-Timoshenko板系的回拉动力学

IF 3 2区数学

Fractional Calculus and Applied Analysis Pub Date : 2025-03-04 DOI: 10.1007/s13540-025-00383-8

Baowei Feng, Mirelson M. Freitas, Anderson J. A. Ramos, Manoel J. Dos Santos

引用次数: 0