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Fractional Differential Calculus最新文献

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On the uniqueness of solutions of two inverse problems for the subdiffusion equation 亚扩散方程两个反问题解的唯一性
Fractional Differential Calculus Pub Date : 2022-05-06 DOI: 10.7153/fdc-2022-12-05
R. Ashurov, Y. Fayziev
{"title":"On the uniqueness of solutions of two inverse problems for the subdiffusion equation","authors":"R. Ashurov, Y. Fayziev","doi":"10.7153/fdc-2022-12-05","DOIUrl":"https://doi.org/10.7153/fdc-2022-12-05","url":null,"abstract":": Let A be an arbitrary positive selfadjoint operator, defined in a separable Hilbert space H . The inverse problems of determining the right-hand side of the equation and the function ϕ in the non-local boundary value problem D ρt u ( t ) + Au ( t ) = f ( t ) (0 < ρ < 1, 0 < t ≤ T ), u ( ξ ) = αu (0) + ϕ ( α is a constant and 0 < ξ ≤ T ), is considered. Operator D t on the left-hand side of the equation expresses the Caputo derivative. For both inverse problems u ( ξ 1 ) = V is taken as the over-determination condition. Existence and uniqueness theorems for solutions of the problems under consideration are proved. The influence of the constant α on the existence and uniqueness of a solution to problems is investigated. An interesting effect was discovered: when solving the forward problem, the uniqueness of the solution u ( t ) was violated, while when solving the inverse problem for the same values of α , the solution u ( t ) became unique.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130399750","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
On solvability of the non-local problem for the fractional mixed-type equation with Bessel operator 带Bessel算子的分数阶混合型方程非局部问题的可解性
Fractional Differential Calculus Pub Date : 2021-11-26 DOI: 10.7153/fdc-2022-12-04
B. Toshtemirov
{"title":"On solvability of the non-local problem for the fractional mixed-type equation with Bessel operator","authors":"B. Toshtemirov","doi":"10.7153/fdc-2022-12-04","DOIUrl":"https://doi.org/10.7153/fdc-2022-12-04","url":null,"abstract":"Fractional differential equations plays a significant role, because of its multiple applications in engineering, chemistry, biology and other parts of science and modeling the real-life problems [1]-[3]. Studying boundary value problems for linear and non-linear fractional differential equations with Riemann-Liouville and Caputo fractional derivative have becoming interesting targets simultaneously [4]-[7]. The quality and the types of articles have been changed when the generalized Riemann-Liouville differential operators (later called Hilfer derivative) used in the scientific field with its interesting application [8], [9]. To tell the truth, the generalization of the Riemann-Lioville fractional differential operators was already announced by M. M. Dzherbashian and A. B. Nersesian [10] in 1968, but because of some reasons it was not familiar with many mathematicians around the globe till the translation of this work published in the journal of Fract. Calc. Appl. An. [11]. We also refer some papers [12]-[13] devoted studying some problems with the Dzherbashian-Nersesian differential operator which has the following form","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125379302","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: 2
Inverse problem of determining an order of the Riemann-Liouville time-fractional derivative 确定Riemann-Liouville时间分数阶导数阶数的反问题
Fractional Differential Calculus Pub Date : 2021-07-28 DOI: 10.7153/fdc-2021-11-14
S. Alimov, R. Ashurov
{"title":"Inverse problem of determining an order of the Riemann-Liouville time-fractional derivative","authors":"S. Alimov, R. Ashurov","doi":"10.7153/fdc-2021-11-14","DOIUrl":"https://doi.org/10.7153/fdc-2021-11-14","url":null,"abstract":"The inverse problem of determining the order of the fractional RiemannLiouville derivative with respect to time in the subdiffusion equation with an arbitrary positive self-adjoint operator having a discrete spectrum is considered. Using the classical Fourier method it is proved, that the value of the norm ||u(t)|| of the solution at a fixed time instance recovers uniquely the order of derivative. A list of examples is discussed, including a linear system of fractional differential equations, differential models with involution, fractional Sturm-Liouville operators, and many others. AMS 2000 Mathematics Subject Classifications : Primary 35R11; Secondary 74S25.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121476448","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: 9
Study of a discretized fractional-order eco-epidemiological model with prey infection 考虑猎物感染的离散分数阶生态流行病学模型研究
Fractional Differential Calculus Pub Date : 2021-04-14 DOI: 10.7153/fdc-2020-10-07
Shuvojit Mondal, Xianbing Cao, N. Bairagi
{"title":"Study of a discretized fractional-order eco-epidemiological model with prey infection","authors":"Shuvojit Mondal, Xianbing Cao, N. Bairagi","doi":"10.7153/fdc-2020-10-07","DOIUrl":"https://doi.org/10.7153/fdc-2020-10-07","url":null,"abstract":". In this paper, an attempt is made to understand the dynamics of a three-dimensional discrete fractional-order eco-epidemiological model with Holling type II functional response. We fi rst discretize a fractional-order predator-prey-parasite system with piecewise constant ar- guments and then explore the system dynamics. Analytical conditions for the local stability of different fi xed points have been determined using the Jury criterion. Several examples are given to substantiate the analytical results. Our analysis shows that stability of the discrete fractional order system strongly depends on the step-size and the fractional order. More speci fi cally, the critical value of the step-size, where the switching of stability occurs, decreases as the order of the fractional derivative decreases. Simulation results explore that the discrete fractional-order system may also exhibit complex dynamics, like chaos, for higher step-size.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"72 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123537261","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 uniqueness determination of the fractional exponents in a three-parameter fractional diffusion 三参数分数扩散中分数指数的唯一性判定
Fractional Differential Calculus Pub Date : 2020-05-18 DOI: 10.7153/fdc-2023-13-04
Ngartelbaye Guerngar, Erkan Nane, S. Ulusoy, H. Wyk
{"title":"A uniqueness determination of the fractional exponents in a three-parameter fractional diffusion","authors":"Ngartelbaye Guerngar, Erkan Nane, S. Ulusoy, H. Wyk","doi":"10.7153/fdc-2023-13-04","DOIUrl":"https://doi.org/10.7153/fdc-2023-13-04","url":null,"abstract":"In this article, we consider the space-time Fractional (nonlocal) diffusion equation $$partial_t^beta u(t,x)={mathtt{L}_D^{alpha_1,alpha_2}} u(t,x), tgeq 0, xin D, $$ where $partial_t^beta$ is the Caputo fractional derivative of order $beta in (0,1)$ and the differential operator ${mathtt{L}_D^{alpha_1,alpha_2}}$ is the generator of a L'evy process, sum of two symmetric independent $alpha_1-$stable and $alpha_2-$stable processes and ${D}$ is the open unit interval in $mathbb{R}$. We consider a nonlocal inverse problem and show that the fractional exponents $beta$ and $alpha_i, i=1,2$ are determined uniquely by the data $u(t, 0) = g(t), 0 < t < T.$ The uniqueness result is a theoretical background for determining experimentally the order of many anomalous diffusion phenomena, which are important in many fields, including physics and environmental engineering. We also discuss the numerical approximation of the inverse problem as a nonlinear least-squares problem and explore parameter sensitivity through numerical experiments.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131576036","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: 2
Unique positive solution for nonlinear Caputo-type fractional q-difference equations with nonlocal and Stieltjes integral boundary conditions 具有非局部和Stieltjes积分边界条件的非线性caputo型分数阶q差分方程的唯一正解
Fractional Differential Calculus Pub Date : 2019-09-01 DOI: 10.7153/fdc-2019-09-19
Ahmad Y. A. Salamooni, D. D. Pawar
{"title":"Unique positive solution for nonlinear Caputo-type fractional q-difference equations with nonlocal and Stieltjes integral boundary conditions","authors":"Ahmad Y. A. Salamooni, D. D. Pawar","doi":"10.7153/fdc-2019-09-19","DOIUrl":"https://doi.org/10.7153/fdc-2019-09-19","url":null,"abstract":"This paper contain a new discussion for the type of generalized nonlinear Caputo fractional $q$-difference equations with $m$-point boundary value problem and Riemann-Stieltjes integral $tilde{alpha}[x]:=int_{0}^{1}~x(t)dLambda(t).$ By applying the fixed point theorem in cones, we investigate an existence of a unique positive solution depends on $lambda>0.$ We present some useful properties related to the Green's function for $m-$point boundary value problem.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126442882","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: 8
Global stability of a Leslie-Gower-type fractional order tritrophic food chain model leslie - gower型分数阶营养食物链模型的全局稳定性
Fractional Differential Calculus Pub Date : 2019-05-27 DOI: 10.7153/FDC-2019-09-11
{"title":"Global stability of a Leslie-Gower-type fractional order tritrophic food chain model","authors":"","doi":"10.7153/FDC-2019-09-11","DOIUrl":"https://doi.org/10.7153/FDC-2019-09-11","url":null,"abstract":"Recently, the dynamical behaviors of a fractional order three species food chain model was studied by Alidousti and Ghahfarokhi ({it Nonlinear Dynamics, doi: org/10.1007/s11071-018-4663-6, 2018}). They proved both the local and global asymptotic stability of all equilibrium points except the interior one. This work extends their work and gives proof of both the local and global stability analysis of the interior equilibrium point. Numerical examples are also provided to substantiate the analytical findings.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"327 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133159410","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: 6
Existence and uniqueness results for generalized Caputo iterative fractional boundary value problems 广义Caputo迭代分数阶边值问题的存在唯一性结果
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2022-12-12
Abdelkrim Salim, M. Benchohra
{"title":"Existence and uniqueness results for generalized Caputo iterative fractional boundary value problems","authors":"Abdelkrim Salim, M. Benchohra","doi":"10.7153/fdc-2022-12-12","DOIUrl":"https://doi.org/10.7153/fdc-2022-12-12","url":null,"abstract":"","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117184341","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
Nonlinear fractional differential equations with $m$-point integral boundary conditions 具有$m$点积分边界条件的非线性分数阶微分方程
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2019-09-05
T. S. Cerdik, N. A. Hamal, Fulya Yoruk Deren
{"title":"Nonlinear fractional differential equations with $m$-point integral boundary conditions","authors":"T. S. Cerdik, N. A. Hamal, Fulya Yoruk Deren","doi":"10.7153/fdc-2019-09-05","DOIUrl":"https://doi.org/10.7153/fdc-2019-09-05","url":null,"abstract":". In this paper, we consider the existence and uniqueness of solution for a fractional order differential equation involving the Riemann-Liouville fractional derivative. By applying some standard fi xed point theorems, we obtain new results on the existence and uniqueness of solution.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"245 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122122533","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: 2
Successive approximations of solutions to the Caputo fractional differential equations 卡普托分数阶微分方程解的逐次逼近
Fractional Differential Calculus Pub Date : 1900-01-01 DOI: 10.7153/fdc-2020-10-10
M. Palani, A. Usachev
{"title":"Successive approximations of solutions to the Caputo fractional differential equations","authors":"M. Palani, A. Usachev","doi":"10.7153/fdc-2020-10-10","DOIUrl":"https://doi.org/10.7153/fdc-2020-10-10","url":null,"abstract":". We consider an initial value problem involving a single term Caputo differential equa- tion of fractional order strictly greater than one. For those with right hand sides that satisfy an Osgood type condition, we show that there exist successive approximations which converge to the solution at an exponential rate. As an application of this result, we study the Ulam-Hyers stability of these problems.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128763238","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
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