Department of Mathematics

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Existence results for a system of fractional differential equations subject to coupled integral boundary conditions
(2017-04-05) Abdul Aleem, Mughal
Recently, Johnny Henderson and Rodica Luca [1], have presented some new existence and uniqueness results, and for this, they have used a variety of theorems. They have worked on fractional di erential equations, and have investigated the uniqueness and existence for non-negative solutions of a system of nonlinear Riemann-Liouville fractional di erential equations D0+v1 (t) + 1f(t; v1(t); v2(t)) = 0; where t 2 (0; 1) and n 1 < 6 n D0+v2 (t) + 2g(t; v1(t); v2(t)) = 0; where t 2 (0; 1); and m 1 < 6 m with the coupled integral boundary conditions v1(0) = v10(0) = = v1n 2 v1(1) = Z 1 (0) = 0; 0 v2(s)dH1(s); v2(0) = v20(0) = = v2m 2 v2(1) = Z 1 (0) = 0; 0 v1(s)dH2(s); where m; n 2 N; m; n > 3; D0+ and D0+ are the derivatives from Riemann-Liouville with orders , respectively. Further, the integrals in the boundary conditions are the integrals from Riemann-Stieltjes. Some adequate conditions will be given on the parameters 1, 2, and nonlinear functions f and g, so that non-negative solutions of the above problem exist. This thesis is detailed review of the results presented in [1].