1. 毕业设计(论文)主要目标:
1. 构造合适的管道解及目标方程的替代函数,替代方程在管道解范围内与目标方程同解;2. 建立合适算子,结合适型微分定义证明替代方程有解存在;3. 证明替代方程的每一个解都在管道解范围内;4. 证明得目标方程解的存在性。
2. 毕业设计(论文)主要内容:
1. 目标分数阶微分方程管道解的建立;2. 替代方程的建立及相关新变量的定义;3. 算子的定义及其紧性证明;4. 替代方程解的存在性证明;5. 替代方程每个解都在管道解范围内的证明;6. 目标方程解的存在性讨论。
3. 主要参考文献
[1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015)57-66.[2] D. R. Anderson, R. I. Avery, Fractional-order boundary value problem with Sturm-Liouville boundary conditions, Electron. J. Differential Equations 2015 (29) (2015) 10.[3] H. Batarfi, J. Losada, J. J. Nieto, W. Shammakh, Three-point boundary value problems for conformable fractional differential equations, J. Funct. Spaces 2015 (2015) 6. Art. ID 706383.[4] J. M. Bebernes, K. Schmitt, Periodic boundary value problem for systems of second order differential equations, J. Differential Equations 13 (1973), 32-47.[5] M. Bohner, C. C. Tisdell, Second order dynamic inclusions, J. Nonlinear Math. Phys. 12(2005) 36-45. suppl. 2.[6] Benaoumeur Bayour, Delfim F. M. Torres, Existence of solution to a local fractional non- linear differential equation. Journal of Computational and Applied Mathematics 312 (2017) 127-133.[7] B. Bayour, A. Hammoudi, D. F. M. Torres, Existence of solution to a nonlinear first-order dynamic equation on time scales, J. Math. Anal. 7 (1) (2016) 31-38.[8] A. Cabada, M. R. Grossinho, F. Minhs, Extremal solutions for third-order nonlinear problemswith upper and lower solutions in reversed order, Nonlinear Anal. 62 (6) (2005) 1109-1121.[9] M. Frigon, Boundary and periodic value problems for systems of nonlinear second orderdifferential equations, Topol. Methods Nonlinear Anal. 1 (2) (1993) 259-274.[10] M. Frigon, H. Gilbert, Existence theorems for systems of third order differential equations,Dynam. Systems Appl. 19 (1) (2010) 1-23.[11] C. Frigon, P. Habets, The Picard boundary value problem for nonlinear second order vectordifferential equations, J. Differentical Equations 42 (1981), 186-198.[12] M. Frigon, H. Gilbert, Existence theorems for systems of third order differential equations,Dynam. Systems Appl. 19 (1) (2010) 1-23.[13] H. Gilbert, Existence theorems for first-order equations on time scales with -Carathodoryfunctions, Adv. Differential Equations 2010 (2010) 20. Art. ID 650827.[14] A. Granas, J. Dugundji, Fixed Point Theory, in: Springer Monographs in Mathematics,Springer, New York, 2003.[15] A. Granas, R. B. Guenther, J. W. lee, Some general existence principle in the Caratheodarytheory of nonlinear differential systems, J. Math. Pures Appl. 70 (1991), 153-196.14.[16] J. R. Graef, L. Kong, F. M. Minhs, J. Fialho, On the lower and upper solution method for higher order functional boundary value problems, Appl. Anal. Discrete Math. 5 (1) (2011)133-146.[17] P. Hartman, On boundary value problems for systems of ordinary, nonlinear, second orderdifferential equations, Trans. Amer. Math. Soc. 96 (1960), 493-509.[18] R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative,J. Comput. Appl. Math. 264 (2014) 65-70.[19] M. Ruyun, Z. Jihui, F. Shengmao, The method of lower and upper solutions for fourth-ordertwo-point boundary value problems, J. Math. Anal. Appl. 215 (2) (1997) 415-422.[20] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Gordon andBreach, Yverdon, 1993.
以上是毕业论文任务书,课题毕业论文、开题报告、外文翻译、程序设计、图纸设计等资料可联系客服协助查找。