Foundations最新文献_第5页

Existence in the Large for Caputo Fractional Multi-Order Systems with Initial Conditions 具有初始条件的Caputo分数阶多阶系统的存在性

Foundations Pub Date : 2023-05-26 DOI: 10.3390/foundations3020021

Z. Denton, A. Vatsala

{"title":"Existence in the Large for Caputo Fractional Multi-Order Systems with Initial Conditions","authors":"Z. Denton, A. Vatsala","doi":"10.3390/foundations3020021","DOIUrl":"https://doi.org/10.3390/foundations3020021","url":null,"abstract":"One of the key applications of the Caputo fractional derivative is that the fractional order of the derivative can be utilized as a parameter to improve the mathematical model by comparing it to real data. To do so, we must first establish that the solution to the fractional dynamic equations exists and is unique on its interval of existence. The vast majority of existence and uniqueness results available in the literature, including Picard’s method, for ordinary and/or fractional dynamic equations will result in only local existence results. In this work, we generalize Picard’s method to obtain the existence and uniqueness of the solution of the nonlinear multi-order Caputo derivative system with initial conditions, on the interval where the solution is bounded. The challenge presented to establish our main result is in developing a generalized form of the Mittag–Leffler function that will cooperate with all the different fractional derivative orders involved in the multi-order nonlinear Caputo fractional differential system. In our work, we have developed the generalized Mittag–Leffler function that suffices to establish the generalized Picard’s method for the nonlinear multi-order system. As a result, we have obtained the existence and uniqueness of the nonlinear multi-order Caputo derivative system with initial conditions in the large. In short, the solution exists and is unique on the interval where the norm of the solution is bounded. The generalized Picard’s method we have developed is both a theoretical and a computational method of computing the unique solution on the interval of its existence.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86287534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Coupled Systems of Nonlinear Proportional Fractional Differential Equations of the Hilfer-Type with Multi-Point and Integro-Multi-Strip Boundary Conditions 具有多点和积分-多条带边界条件的hilfer型非线性比例分数阶微分方程耦合系统

Foundations Pub Date : 2023-05-24 DOI: 10.3390/foundations3020020

S. Ntouyas, Bashir Ahmad, J. Tariboon

引用次数: 2

Emergent Gravity Simulations for Schwarzschild–de Sitter Scenarios Schwarzschild-de Sitter情景下的紧急重力模拟

Foundations Pub Date : 2023-05-14 DOI: 10.3390/foundations3020019

A. Keppens

引用次数: 0

Different Mass Definitions and Their Pluses and Minuses Related to Gravity 不同的质量定义及其与重力相关的优缺点

Foundations Pub Date : 2023-04-18 DOI: 10.3390/foundations3020017

E. Haug

引用次数: 4

Using the Carnivorous Sponge Lycopodina hypogea as a Nonclassical Model for Understanding Apoptosis-Mediated Shape Homeostasis at the Organism Level 利用肉食性海绵Lycopodina hypogea作为非经典模型在生物体水平上理解细胞凋亡介导的形状稳态

Foundations Pub Date : 2023-04-18 DOI: 10.3390/foundations3020018

S. Baghdiguian, E. Le Goff, L. Paradis, J. Vacelet, N. Godefroy

{"title":"Using the Carnivorous Sponge Lycopodina hypogea as a Nonclassical Model for Understanding Apoptosis-Mediated Shape Homeostasis at the Organism Level","authors":"S. Baghdiguian, E. Le Goff, L. Paradis, J. Vacelet, N. Godefroy","doi":"10.3390/foundations3020018","DOIUrl":"https://doi.org/10.3390/foundations3020018","url":null,"abstract":"The dynamic equilibrium between death and regeneration is well established at the cell level. Conversely, no study has investigated the homeostatic control of shape at the whole organism level through processes involving apoptosis. To address this fundamental biological question, we took advantage of the morphological and functional properties of the carnivorous sponge Lycopodina hypogea. During its feeding cycle, this sponge undergoes spectacular shape changes. Starved animals display many elongated filaments to capture prey. After capture, prey are digested in the absence of any centralized digestive structure. Strikingly, the elongated filaments actively regress and reform to maintain a constant, homeostatically controlled number and size of filaments in resting sponges. This unusual mode of nutrition provides a unique opportunity to better understand the processes involved in cell renewal and regeneration in adult tissues. Throughout these processes, cell proliferation and apoptosis are interconnected key actors. Therefore, L. hypogea is an ideal organism to study how molecular and cellular processes are mechanistically coupled to ensure global shape homeostasis.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90790521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Comparison Result for the Nabla Fractional Difference Operator Nabla分数差分算子的一个比较结果

Foundations Pub Date : 2023-04-12 DOI: 10.3390/foundations3020016

J. Jonnalagadda

引用次数: 0

Controllability of a Class of Heterogeneous Networked Systems 一类异构网络系统的可控性

Foundations Pub Date : 2023-04-06 DOI: 10.3390/foundations3020015

Abhijith Ajayakumar, R. K. George

引用次数: 0

A Newton-like Midpoint Method for Solving Equations in Banach Space Banach空间中求解方程的类牛顿中点法

Foundations Pub Date : 2023-03-27 DOI: 10.3390/foundations3020014

Samundra Regmi, I. Argyros, Gagan Deep, Laxmi Rathour

引用次数: 1

Extended Convergence of Two Multi-Step Iterative Methods 两种多步迭代法的扩展收敛性

Foundations Pub Date : 2023-03-13 DOI: 10.3390/foundations3010013

Samundra Regmi, I. Argyros, Jinny Ann John, Jayakumar Jayaraman

{"title":"Extended Convergence of Two Multi-Step Iterative Methods","authors":"Samundra Regmi, I. Argyros, Jinny Ann John, Jayakumar Jayaraman","doi":"10.3390/foundations3010013","DOIUrl":"https://doi.org/10.3390/foundations3010013","url":null,"abstract":"Iterative methods which have high convergence order are crucial in computational mathematics since the iterates produce sequences converging to the root of a non-linear equation. A plethora of applications in chemistry and physics require the solution of non-linear equations in abstract spaces iteratively. The derivation of the order of the iterative methods requires expansions using Taylor series formula and higher-order derivatives not present in the method. Thus, these results cannot prove the convergence of the iterative method in these cases when such higher-order derivatives are non-existent. However, these methods may still converge. Our motivation originates from the need to handle these problems. No error estimates are given that are controlled by constants. The process introduced in this paper discusses both the local and the semi-local convergence analysis of two step fifth and multi-step 5+3r order iterative methods obtained using only information from the operators on these methods. Finally, the novelty of our process relates to the fact that the convergence conditions depend only on the functions and operators which are present in the methods. Thus, the applicability is extended to these methods. Numerical applications complement the theory.","PeriodicalId":81291,"journal":{"name":"Foundations","volume":"78 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73081739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Extended Convergence for Two Sixth Order Methods under the Same Weak Conditions 两个六阶方法在相同弱条件下的扩展收敛性

Foundations Pub Date : 2023-03-10 DOI: 10.3390/foundations3010012

I. Argyros, Samundra Regmi, Jinny Ann John, Jayakumar Jayaraman

引用次数: 1