Existence of Solution for a Coupled System of Fractional Integro-Differential Equations on an Unbounded Domain
Existence of Solution for a Coupled System of Fractional Integro-Differential Equations on an Unbounded Domain
摘要
We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arzela-Ascoli theorem to show a fixed point theorem of Schauder.
We present the existence of solution for a coupled system of fractional integro-differential equations. The differential operator is taken in the Caputo fractional sense. We combine the diagonalization method with Arzela-Ascoli theorem to show a fixed point theorem of Schauder.
参考文献25
-
1W. G. Glockle and T. F. Nonnenmacher, A Fractional calculus approach of self-similar protein dynamics, Biophys. J., 68 (1995), 46--53.
-
2R. Hilfer, Applications of Fractional Calculus in Phisics, World Scientific, Singapore, 2000.
-
3E Metzler, W. Schick, H. G. Kilian and T. F. Nonnenmacher, Relaxation in filled polymers: a fractional calculus approach, J. Chem. Phys., 103 (1995), 7180-7186.
-
4K. B. Miller and B. Ross, An Introduction to the Fractional Calculus and Fractional Differen- tial Equations, Wiely New york, 1993.
-
5I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
-
6D. Baleanu, A. K. Golmankhaneh and R. Nigmatullin, Fractional Newtonian mechanics, Central Euro. J. Phys., 8 (2010), 120-125.
-
7S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, Yverdon, 1993.
-
8B. N. Lundstrom, M. H. Higgs, W. J. Spain and A. L. Fairhall, Fractional differentiation by neocortical pyramidal neurons, Nature Neurosci., 11( 11 ) (2008).
-
9I. Poudlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Fract. Calc. Appl. Anal., 5 (2002), 367-386.
-
10A. A. Kilbas, M. Hari and Juan J. Srivastava. Trujillo, Theory and Applications of Fractional Differential Equations, in: Nrth-Holland Mathematics Studies, 204 (2006), Elsevier Science B. V, Amesterdam.
-
1Yong Li (Dept. of Math. and Computer, Chongqing Normal University, Chongqing 400047.EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL STOCHASTIC DIFFERENTIAL EQUATIONS WITH DELAY[J].Annals of Differential Equations,2010,26(2):181-189.
-
2丁孙荭.EXISTENCE OF SOLUTION FOR A KIND OF BOUNDARY VALUE PROBLEM WITH JUMPING CHARACTER[J].Chinese Science Bulletin,1988,33(16):1322-1325.
-
3廉玉婷,高云兰,李晓宇,王国君.一类奇异三阶微分方程三点边值问题正解的存在性[J].内蒙古工业大学学报(自然科学版),2015,34(2):87-91. 被引量:1
-
4高永馨,汪凤琴.三阶非线性微分方程三点边值问题解的存在性(英文)[J].黑龙江大学自然科学学报,2015,32(4):421-427. 被引量:7
-
5王俊霞.分数阶初值问题解的存在性[J].河南大学学报(自然科学版),2015,45(5):528-532.
-
6Shi Ai-ling,Zhang Shu-qin,Li Yong.Existence of Solution for Fractional Differential Problem with a Parameter[J].Communications in Mathematical Research,2014,30(2):157-167.
-
7陶继成.THE BOUNDARY VALUE PROBLEMS OF ELLIPTICSYSTEM (E_1) ON THE UNBOUNDED DOMAIN[J].Acta Mathematica Scientia,2002,22(1):123-130.
-
8李文深.THE UNIQUENESS AND EXISTENCE OF SOLUTION OF THE CHABACTERISTIC PROBLEM ON THE GENERALIZED KdV EQUATION[J].Applied Mathematics and Mechanics(English Edition),1994,15(5):491-498.
-
9Yong Li (Institute of Math. and Computer Science, Chongqing Normal University, Chongqing 400047).EXISTENCE OF SOLUTION TO NONLINEAR SECOND ORDER NEUTRAL DIFFERENTIAL SYSTEM WITH DELAY[J].Annals of Differential Equations,2010,26(4):429-435.
-
10张淑琴.EXISTENCE OF SOLUTION FOR A BOUNDARY VALUE PROBLEM OF FRACTIONAL ORDER[J].Acta Mathematica Scientia,2006,26(2):220-228. 被引量:27