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The Existence of Solutions for a Fractional 2m-Point Boundary Value Problems

Gang Wang, Wenbin Liu, Jinyun Yang, Sinian Zhu, Ting Zheng
2012 Journal of Applied Mathematics  
A new result on the existence of solutions for above fractional boundary value problem is obtained.  ...  By using the coincidence degree theory, we consider the following 2m-point boundary value problem for fractional differential equationD0+αut=ft,ut,D0+α-1ut,D0+α-2ut+et,0<t<1,I0+3-αut|t=0=0,D0+α-2u1=∑i=  ...  Acknowledgments This work is sponsored by NNSF of China 10771212 and the Fundamental Research Funds for the Central Universities 2010LKSX09 .  ... 
doi:10.1155/2012/841349 fatcat:3uz3mldep5dyhdfnspsz3rz7ly

The Thin Obstacle Problem: A Survey [article]

Xavier Fernández-Real
2020 arXiv   pre-print
We present the theory with some proofs: from the optimal regularity of solutions and classification of free boundary points, to more recent results on the non-regular part of the free boundary and generic  ...  In this work we present a general introduction to the Signorini problem (or thin obstacle problem).  ...  They do exist: the homogeneous solutions are themselves examples of solutions to the thin obstacle problem with free boundary points belonging to Γ half (u).  ... 
arXiv:2011.03299v1 fatcat:uwywj6i5zrcgtppgk3afkfcu3e

About the Nature of the Spectrum of the Periodic Problem for the Heat Equation with a Deviating Argument

I. Orazov, A. Shaldanbayev, M. Shomanbayeva
2013 Abstract and Applied Analysis  
We study the nature of the spectrum of the periodic problem for the heat equation with a lower-order term and with a deviating argument.  ...  A significant influence of the lower-order term on the correct solvability of this problem is found. We obtain a criterion for the strong solvability of the above-mentioned problem.  ...  Acknowledgments The authors are grateful to the referees for their critical comments which helped in improving the content of this paper.  ... 
doi:10.1155/2013/128363 fatcat:uyu5sdmgtbhxnojftmjlgyku2m

On a system of fractional coupled hybrid Hadamard differential equations with terminal conditions

Karthikeyan Buvaneswari, Panjaiyan Karthikeyan, Dumitru Baleanu
2020 Advances in Difference Equations  
In this manuscript, we study the existence of solutions for a coupled system of nonlinear hybrid differential equations of fractional order involving Hadamard derivative with nonlocal boundary conditions  ...  By using suitable fixed point theorems we establish sufficient conditions for the existence result. An example is provided to illustrate our main result. MSC: Primary 34A08; secondary 34B18  ...  Acknowledgements The authors express their gratitude to the referees for their helpful suggestions, which improved the final version of this paper. Funding Not applicable.  ... 
doi:10.1186/s13662-020-02790-y fatcat:uzjd3wpslzdjtnrbkacjk7gd4y

A fixed point approach to the solution of singular fractional differential equations with integral boundary conditions

Kalaivani Chandran, Kalpana Gopalan, Sumaiya Tasneem Zubair, Thabet Abdeljawad
2021 Advances in Difference Equations  
Eventually, we investigate the existence and uniqueness of solutions of the aforementioned boundary value problem of order α via a fixed point problem of an integral operator.  ...  Thereafter, we specifically consider a following boundary value problem (BVP) for a singular fractional differential equation of order α: $$ \begin{aligned} &{}^{c}D^{\alpha }v(t) + h \bigl(t,v(t) \bigr  ...  The first, second and third authors would like to thank the Management of Sri Sivasubramaniya Nadar College of Engineering, Kalavakkam-603110, for their continuous support and encouragement to carry out  ... 
doi:10.1186/s13662-021-03225-y fatcat:mywfnipqz5g65eo3xlrr7nsnza

Page 7120 of Mathematical Reviews Vol. , Issue 94m [page]

1994 Mathematical Reviews  
The global existence of regular solutions, classical solutions and C-solutions of the periodic boundary problem (1), (4) and the initial value problem (1), (28) are studied. Nicolai N.  ...  (UZ-TASH; Tashkent) On a boundary value problem for an equation with a fractional derivative. (Russian) Dokl. Akad. Nauk 333 (1993), no. 4, 446-448.  ... 

Spectral Fractional Laplacian with Inhomogeneous Dirichlet Data: Questions, Problems, Solutions [article]

Stanislav Harizanov and Svetozar Margenov and Nedyu Popivanov
2020 arXiv   pre-print
For comparing the differences between the solutions in the spectral and Riesz formulations, we consider an inhomogeneous fractional Dirichlet problem.  ...  The real challenge however represents the case when this equation is posed in a bounded domain Ω and proper boundary conditions are needed for the correctness of the corresponding problem.  ...  problems -a homogeneous fractional Dirichlet problem for the operator, given by (3) and an inhomogeneous fractional Dirichlet problem, for which we are looking for the solution of the standard non-fractional  ... 
arXiv:2010.01383v1 fatcat:lybdpmxxhrbglghnzi2cjmuavm

On a coupled Caputo conformable system of pantograph problems

2020 Turkish Journal of Mathematics  
Our fundamental purpose in the present manuscript is to explore existence and uniqueness criteria for a new coupled Caputo conformable system of pantograph problems in which for the first time, the given  ...  In the final part, a simulative example is designed to cover the applicability aspects of theoretical findings available in this research manuscript from a numerical point of view.  ...  Acknowledgments The second and third authors were supported by Azarbaijan Shahid Madani University.  ... 
doi:10.3906/mat-2010-70 fatcat:d47qbqjqhzaexpyrnh2lwl4gsa

Existence of positive solutions for a high order fractional differential equation integral boundary value problem with changing sign nonlinearity

Jiankun He, Mei Jia, Xiping Liu, Hui Chen
2018 Advances in Difference Equations  
In this paper, we investigate the existence of positive solutions for a class of high order fractional differential equation integral boundary value problems with changing sign nonlinearity.  ...  By applying cone expansion and cone compression fixed point theorem, we have obtained and proved theorems related to the existence of positive solutions, which highlight the influences of the parameters  ...  Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 11171220) and the Hujiang Foundation of China (B14005).  ... 
doi:10.1186/s13662-018-1465-6 fatcat:zimnsqb55bafvjgamnynhr2iky

Page 1947 of Mathematical Reviews Vol. , Issue 85e [page]

1985 Mathematical Reviews  
A boundary value problem for an elliptic equation of order 2m is considered in a plane polygonal domain.  ...  [Analytic right-hand side for an elliptic boundary value problem of order 2m on a polygon] Comm. Partial Differential Equations 9 (1984), no. 2, 169-195.  ... 

Boundary value problems for impulsive fractional differential equations in Banach spaces

Shuai Yang, Shuqin Zhang
2017 Filomat  
This paper is devoted to studying the existence and uniqueness of solutions to the boundary value problems for a impulsive fractional differential equation in Banach spaces.  ...  The arguments are based upon the methods of noncompact measure, Banach fixed point theorem and Krasnoselskii's fixed point theorem.  ...  Acknowledgements This work is supported by the National Natural Science Foundation of China (11371364). The author is very grateful to the anonymous referee for his or her valuable suggestions.  ... 
doi:10.2298/fil1718603y fatcat:wosa23l4wzbfzo63lx6onm34oq

Approximate Solutions for Fractional Boundary Value Problems via Green-CAS Wavelet Method

Muhammad Ismail, Umer Saeed, Jehad Alzabut, Mujeeb ur Rehman
2019 Mathematics  
Sufficient conditions for the existence of unique solutions are established for the boundary value problem under consideration.  ...  In this study, we present a novel numerical scheme for the approximate solutions of linear as well as non-linear ordinary differential equations of fractional order with boundary conditions.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math7121164 fatcat:jxctnimzrzbyjaccxsxkyrldky

Page 2239 of Mathematical Reviews Vol. , Issue 84f [page]

1984 Mathematical Reviews  
This article is concerned with the existence of weak solutions of boundary value problems for quasilinear operators in divergence form Au= > (-1)"D%,(x,u, Vu,--> V"u)=f jajsm is an open domain Q of R”.  ...  A. 84f:35059 The behavior near the boundary of solutions of second-order quasilinear elliptic equations. (Russian) Boundary value problems for partial differential equations, 31-38, Azerbaidzhan.  ... 

Page 902 of Mathematical Reviews Vol. , Issue 90B [page]

1990 Mathematical Reviews  
He obtains the following results: (1) For m <n the inhomogeneous problem A is always solvable, and the corresponding homogeneous problem (F =0,h =0) has 2m2m + 1 linearly independent solutions; (2)  ...  Assuming that w(s) = w(z)|,¢2, is a boundary value of the function that is inverse to z(w), and the parameter s is an arc abscissa of a point of the contour L, that corresponds to the point w(s) € L,,,  ... 

Existence of Concave Positive Solutions for Boundary Value Problem of Nonlinear Fractional Differential Equation withp-Laplacian Operator

Jinhua Wang, Hongjun Xiang, ZhiGang Liu
2010 International Journal of Mathematics and Mathematical Sciences  
By using fixed point theorem, the results for existence and multiplicity of concave positive solutions to the above boundary value problem are obtained.  ...  We consider the existence and multiplicity of concave positive solutions for boundary value problem of nonlinear fractional differential equation withp-Laplacian operatorD0+γ(ϕp(D0+αu(t)))+f(t,u(t),D0+  ...  Acknowledgments This work was jointly supported by the Natural Science Foundation of Hunan Provincial under Grants 09JJ3005 and 2009JT3042, the Construct Program of the Key Discipline in Hunan Province  ... 
doi:10.1155/2010/495138 fatcat:mrlcs4fj2bal7fzsso5gvpftkm
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