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Existence Results for Fractional Evolution Systems with Riemann-Liouville Fractional Derivatives and Nonlocal Conditions

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Based on concepts for semigroup theory, fractional calculus, Banach contraction principle and Krasnoselskii fixed point theorem (FPT), this manuscript is principally involved with existence results of Riemann-Liouville (RL) fractional neutral integro-differential systems (FNIDS) with nonlocal conditions (NLCs) in Banach spaces. An example is offered to demonstrate the theoretical concepts.
Wydawca
Rocznik
Strony
487--504
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore - 641 042, Tamil Nadu, India
  • Department of Mathematics, C. B. M. College, Kovaipudur, Coimbatore - 641 042, Tamil Nadu, India
autor
  • Department of Mathematics, Hindusthan College of Arts and Science, Behind Nava India, Coimbatore - 641 028, Tamil Nadu, India
autor
  • Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
Bibliografia
  • [1] Baleanu D, Machado JAT, Luo ACJ. Fractional Dynamics and Control. Springer. New York. USA. 2012. ISBN 978-1-4614-0457-6, 978-1-4614-0456-9. URL http://www.springer.com/la/book/9781461404569.
  • [2] Kilbas AA, Srivastava HM and Trujillo JJ. Theory and Applications of Fractional Differential Equations, vol. 204. Elsevier. Amsterdam. 2006. ISBN: 9780444518323.
  • [3] Zhou Y. Basic Theory of Fractional Differential Equations. World Scientific. Singapore. 2014. ISBN: 978-9814579896.
  • [4] Podlubny I. Fractional Differential Equations. Academic Press. New York. 1999. ISBN: 012558840.
  • [5] Hernandez E, Regan D. O’ and Balachandran K. On recent developments in the theory of abstrac differential equations with fractional derivatives. Nonlinear Analysis. 2010; 73: 3462-3471. URL http://dx.doi.org/10.1016/j.na.2010.07.035.
  • [6] Zhou Y and Jiao F. Existence of mild solutions for fractional neutral evolution equations. Computers with Mathematics and Applications. 2010; 59 (3): 1063-1077. URL http://dx.doi.org/10.1016/j.camwa.2009.06.026.
  • [7] Balachandran K and Kiruthika S. Existence results for fractional integrodifferential equations with nonlocal condition via resolvent operators. Computers and Mathematics with Applications. 2011; 62: 1350-1358. URL http://dx.doi.org/10.1016/j.camwa.2011.05.001.
  • [8] Agarwal RP, Dos Santos JPC and Cuevas C. Analytic resolvent operator and existence results for fractional integro-differential equations. Journal of Abstract Differential Equation and Applications. 2012; 2 (2): 26-47. URL http://math-res-pub.org/jadea/2/2/analytic resolvent-operator-and-existence-results-fractional-integro-differential.
  • [9] Wang JR, Wei W and Feckan M. Nonlocal Cauchy problems for fractional evolution equations involving Volteraa-Fredholm type integral operators. Miskolc Mathematical Notes. 2012; 13 (1): 127-147. URL http://mat76.mat.uni-miskolc.hu/mnotes/article/457.
  • [10] Yudong Z, Xiaojun Y, Carlo C, Ravipudi Venkata R, Shuihua W and Preetha P. Tea category identification using a novel fractional fourier entropy and jaya algorithm. Entropy. 2016; 18 (3): 77. doi: 10.3390/e18030077.
  • [11] Shuihua W, Yudong Z, Xiaojun Y, Ping S, Zhengchao D, Aijun L and Ti-Fei Y. Pathological brain detection by a novel image feature fractional fourier entropy. Entropy. 2015: 17 (12): 8278-8296. doi: 10.3390/e17127877.
  • [12] Byszewski L. Theorems about existence and uniqueness of solutions of a semi-linear evolution nonlocal Cauchy problem. Journal of Mathematical Analysis and Applications. 1991; 162: 494-505. URL http://dx.doi.org/10.1016/0022-247X(91)90164-U.
  • [13] Byszewski L and Lakshmikantham V. Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space. Applicable Analysis. 1991; 40: 11-19. URL http://dx.doi.org/10.1080/00036819008839989.
  • [14] Heymans N and Podlubny I. Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta. 2006; 45: 765-771. doi: 10.1007/s00397-005-0043-5.
  • [15] Li F, Liang J and Xu HK. Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions. Journal of Mathematical Analysis and Applications. 2012; 391: 510-525. doi: 10.1016/j.jmaa.2012.02.057.
  • [16] Liu ZH and Li XW. Existence and uniqueness of solutions for the nonlinear impulsive fractional differential equations. Communications in Nonlinear Science and Numerical Simulation. 2013; 18: 1362-1373. doi: 10.1016/j.cnsns.2012.10.010.
  • [17] Liu ZH and Li XW. On the controllability of impulsive fractional evolution inclusions in Banach spaces. Journal of Optimization Theory and Applications. 2013; 156: 167-182. doi: 10.1007/s10957-012-0236-x.
  • [18] Liu ZH and Wang R. A note on fractional equations of Volterra type with nonlocal boundary condition. Abstract and Applied Analysis. 2013. Article ID 432941. URL http://dx.doi.org/10.1155/2013/432941.
  • [19] Wang JR. Zhou Y and Feckan M. Abstract Cauchy problem for fractional differential equations. Nonlinear Dynamics. 2013; 71: 685-700. doi: 10.1007/s11071-012-0452-9.
  • [20] Zhou Y and Jiao F. Existence of mild solutions for fractional neutral evolution equations. Computers with Mathematics and Applications. 2010; 59: 1063-1077. URL http://dx.doi.org/10.1016/j.camwa.2009.06.026.
  • [21] Zhou Y, Jiao F and Li J. Existence and uniqueness for fractional neutral differential equations with infinite delay. Nonlinear Analysis. 2009; 71: 3249-3256. URL http://dx.doi.org/10.1016/j.na.2009.01.202.
  • [22] Zhou Y, Jiao F and Li J. Existence and uniqueness for p-type fractional neutral differential equations. Nonlinear Analysis. 2009; 71: 2724-2733. URL http://dx.doi.org/10.1016/j.na.2009.01.105.
  • [23] Liu ZH, Sun JH and Szanto I. Monotone iterative technique for Riemann-Liouville fractional integro-differential equations with advanced arguments. Results Mathematics. 2013; 63: 1277-1287. doi: 10.1007/s00025-012-0268-4.
  • [24] Zhou Y, Zhang L and Shen XH. Existence of mild solutions for fractional evolution equations. Journal of Integral Equations and Applications. 2013; 25: 557-585. doi: 10.1216/JIE-2013-25-4-557.
  • [25] Agarwal RP, Belmekki M and Benchohra M. A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative. Advances in Difference Equations. 2009: Article ID 981728. doi: 10.1155/2009/981728.
  • [26] Liu YL and Lv JY. Existence results for Riemann-Liouville fractional neutral evolution equations. Advances in Difference Equations. 2014; (1): 83. doi: 10.1186/1687-1847-2014-83.
  • [27] Liu Z and Li X. Approximate controllability of fractional evolution systems with Riemann-Liouville fractional derivatives. SIAM Journal of Control Optimizations. 2015; 53 (1): 1920-1933. doi: 10.13140/RG.2.1.1732.0806.
  • [28] Yang M and Wang Q. Approximate controllability of Riemann-Liouville fractional differentia inclusions. Applied Mathematics and Computation. 2016; 274: 267-281. doi: 10.1016/j.amc.2015.11.017.
  • [29] Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer. New York, 1983. ISBN: 978-1-4612-5563-5, 978-1-4612-5561-1.
  • [30] Wang JR and Zhou Y. Existence and controllability results for fractional semilinear differential inclusions. Nonlinear Analysis. 2011; 12 (6): 3642-3653. URL http://dx.doi.org/10.1016/j.nonrwa.2011.06.021.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0229a9d9-8030-4b91-8d66-93c6fa50aa78
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