Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P502
J. A.Nanware, B.D. Dawka, "Method of Lower and Upper Solutions for Differential Equations of Fractional Order with Integral Boundary Conditions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 8-13, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P502
System of Riemann-Liouville fractional differential equations with integral boundary conditions is considered. Method of lower and upper solutions is developed for system of Riemann-Liouville fractional differential equations with integral boundary conditions. Method is successfully employed to study existence and uniqueness results for the problem.
[1] Debnath Lokenath, Bhatta Dambaru : Integral Transforms and Their Applications, Second Edition, Taylor and Francis Group, New York, 2007.
[2] Jankwoski T., “Differential Equations with Integral Boundary Conditions”, Journal of Computational and Applied Mathematics 147 pp 1-8,2012
[3] Kilbas A. A., Srivastava H. M., and Trujillo J. J., Theory and Applications of Fractional Differential Equations, North Holland Mathematical Studies Vol.204. Elsevier(North-Holland) Sciences Publishers, Amsterdam,2006.
[4] Ladde G. S., Lakshmikantham V., Vatsala A. S., Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman Advanced Publishing Program, London, 1985.
[5] Lakshmikantham V., Vatsala A. S.: Theory of Fractional Differential Equations and Applications, Commun.Appl.Anal. 11(2007)395-402.
[6] Lakshmikantham V., Vatsala A. S.,”Basic Theory of Fractional Differential Equations and Applications”, Non. Anal. 69, no.8, pp 2677-2682, 2008.
[7] Lakshmikantham V., Vatsala A. S.,”General Uniqueness and Monotone Iterative Technique for Fractional Differential Equations,” Appl.Math. Lett. 21, no.8, pp 828-834, 2008.
[8] Lakshmikantham V., Leela S.: Differential and Integral Inequalities, Vol.I, Academic Press, New York, 1969.
[9] Lakshmikantham V., Leela S. and Devi J. V.: Theory and Applications of Fractional Dynamical Systems, Cambridge Scientific Publishers Ltd, 2009.
[10] McRae F. A.,” Monotone Iterative Technique and Existence Results for Fractional Differential Equations, Non. Anal. 71(12) pp 6093-6096, 2009.
[11] F.A.McRae, “Monotone Method for Periodic Boundary Value Problems of Caputo Fractional Differential Equations”, Commun.Appl.Anal.14(1) pp 73-80,2010.
[12] J.A. Nanware, “Existence and Uniqueness Results for Fractional Differential Equations Via Monotone Method,” Bull.Marathwada Math.Soc.14(1),pp 39-56 ,2013.
[13] J.A.Nanware, Monotone Method In Fractional Differential Equations and Applications, Dr.Babsaheb Ambedkar Marathwada University, Ph.D Thesis, 2013.
[14] J.A.Nanware, D.B.Dhaigude, “Boundary Value Problems for Differential Equations of Non-integer Order Involving Caputo Fractional Derivative,” Advanced Studies in Contemporary Mathematics, 24(3), pp 369-376,2014.
[15] J.A.Nanware, D.B.Dhaigude, “Monotone Iterative Scheme for System of Riemann-Liouville Fractional Differential Equations with Integral Boundary Conditions” , Math.Modelling Sci.Compu., Vol.283 (2012), 395-402 , Springer-Verlag.
[16] Oldham K. B., Spanier J.: The Fractional Calculus,Dover Publications, INC, New York, 2002.
[17] Podlubny I.: Fractional Differential Equations, Academic Press, San Diego, 1999.
[18] Wang T. and Xie “ Existence and Uniqueness of Fractional Differential Equations with Integral Boundary Conditions”, The Journal of Nonlinear Sciences and Applications, 1 no.4, pp 206-212,2008.
[19] Wang X., Wang L., Zeng Q.,” Fractional Differential Equations with Integral Boundary Conditions”, The Journal of Nonlinear Sciences and Applications, 8(4), pp 309-314,2015.