Integrable solutions for implicit fractional order differential equations with nonlocal condition

References

• R. P. Agarwal, M. Belmekki and M. Benchohra, A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative. Adv Differ. Equat. 2009(2009) Article ID 981728, 1–47.
   Web of Science ®Google Scholar
• R.P Agarwal, M. Benchohra and S. Hamani, A survey on existence result for boundary value problems of nonlinear fractional differential equations and inclusions, Acta. Appl. Math. 109 (3) (2010), 973–1033. doi: 10.1007/s10440-008-9356-6
   Web of Science ®Google Scholar
• S. Abbas, M. Benchohra and G.M. N’Guérékata, Topics in Fractional Differential Equations, Springer, New York, 2012.
   Google Scholar
• S. Abbas, M. Benchohra and G.M. N’Guérékata, Advanced Fractional Differential and Integral Equations, Nova Science Publishers, New York, 2014.
   Google Scholar
• D. Baleanu, K. Diethelm, E. Scalas, J.J. Trujillo, Fractional Calculus Models and Numerical Methods, World Scientific Publishing, New York, 2012.
   Google Scholar
• M. Benchohra and B. A. Slimani. Existence And Uniqueness Of Solutions To Impulsive Fractional Differential Equations. Electronic Journal of Differential Equations, (2009) 10, 1–11.
   Google Scholar
• M. Benchohra, S. Hamani and S.K. Ntouyas, Boundary value problems for differential equations with fractional order, Surveys Math. Appl. 3 (2008), 1–12.
   Google Scholar
• M. Benchohra and M. S. Souid, Integrable Solutions For Implicit Fractional Order Functional Differential Equations with Infinite Delay, Archivum Mathematicum (BRNO) Tomus 51 (2015), 67–76 . doi: 10.5817/AM2015-2-67
   Web of Science ®Google Scholar
• M. Benchohra and M. S. Souid, L1 -Solutions of Boundary Value Problems for Implicit Fractional Order Differential Equations, Surveys in Mathematics and its Applications 10 (2015), 49–59.
   Google Scholar
• M. Benchohra and M. S. Souid. L1 -Solutions for Implicit Fractional Order Differential Equations with Nonlocal Conditions. Filomat, 30(6), (2016) 1485–1492. doi: 10.2298/FIL1606485B
   Web of Science ®Google Scholar
• R. F. Brown, M. Furi, L. Górniewicz, B. Jiang, Handbook of Topological Fixed Point Theory, Springer-Verlag, 2005.
   Google Scholar
• K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.
   Google Scholar
• A. M. A. El-Sayed, Sh. A. Abd El-Salam, Lp -solution of weighted Cauchy-type problem of a differ-integral functional equation, Intern. J. Nonlinear Sci. 5 (2008) 281–288.
   Google Scholar
• A.M.M. El-Sayed, H.H.G. Hashem, Integrable and continuous solutions of a nonlinear quadratic integral equation, Electron. J. Qual. Theory Differ. Equ. 2008, No. 25, 1–10.
   Google Scholar
• L. Byszewski, Theorems about existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494–505. doi: 10.1016/0022-247X(91)90164-U
   Web of Science ®Google Scholar
• L. Byszewski, Existence and uniqueness of mild and classical solutions of semilinear functional-differential evolution nonlocal Cauchy problem. Selected problems of mathematics, 25-33, 50 th Anniv. Cracow Univ. Technol. Anniv. Issue, 6, Cracow Univ. Technol. Krakw, 1995
   Google Scholar
• L. Byszewski and V. Lakshmikantham, Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Appl. Anal. 40 (1991), 11–19. doi: 10.1080/00036819008839989
   Google Scholar
• R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
   Google Scholar
• A.A. Kilbas, Hari M. Srivastava, and Juan J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, 204. Elsevier Science B.V., Amsterdam, 2006.
   Google Scholar
• V. Lakshmikantham, J.V. Devi, Theory of fractional differential equations in a Banach space, Eur. J. Pure Appl. Math. 1 (2008) 38–45.
   Google Scholar
• V. Lakshmikantham, S. Leela and J. Vasundhara, Theory of Fractional Dynamic Systems, Cambridge Academic Publishers, Cambridge, 2009.
   Google Scholar
• F. Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity. An introduction to mathematical models. Imperial College Press, London, 2010.
   Google Scholar
• K.B. Oldham and J. Spanier, The Fractional Calculus, Academic Press, New York, London, 1974.
   Google Scholar
• M. D. Ortigueira, Fractional Calculus for Scientists and Engineers. Lecture Notes in Electrical Engineering, 84. Springer, Dordrecht, 2011.
   Google Scholar
• I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
   Google Scholar
• M. S. Souid. L1 -Solutions of Boundary Value Problems for Implicit Fractional Order Differential Equations with Integral Conditions. International Journal of Advanced Research in Mathematics, 11, (2018) 8–17. doi: 10.18052/www.scipress.com/IJARM.11.8
   Google Scholar
• V. E. Tarasov, Fractional Dynamics: Application of Fractional Calculus to Dynamics of Particles, Fields and Media, Springer, Heidelberg; Higher Education Press, Beijing, 2010.
   Google Scholar
• U. Witthayarat, K. Wattanawitoon and P. Kumam (2016) Iterative Scheme for System of Equilibrium Problems and Bregman Asymptotically Quasi-Nonexpansive Mappings in Banach Spaces, Journal of Information and Optimization Sciences, 37:3, 321–342, DOI: 10.1080/02522667.2014.932093
   Web of Science ®Google Scholar