Department of Mathematics

Permanent URI for this collection

Now showing 1 - 1 of 1

Existence results for a system of fractional differential equations subject to coupled integral boundary conditions
(University of Management and Technology Lahore, 2016) Mughal, Abdul Aleem
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 differential equations, and have investigated the uniqueness and existence for non-negative solutions of a system of nonlinear Riemann-Liouville fractional differential equations α v1(t) + λ1f (t, v1(t), v2(t)) = 0, where t ∈ (0, 1) and n − 1 < α ™ n β v2(t) + λ2g(t, v1(t), v2(t)) = 0, where t ∈ (0, 1), and m − 1 < β ™ m with the coupled integral boundary conditions j n−2 ∫ 1 j m−2 ∫ 1 where m, n ∈ N ; m, n “ 3; Dα and Dβ are the derivatives from Riemann-Liouville with orders α, β respectively. Further, the integrals in the boundary conditions are the integrals from Riemann-Stieltjes. Some adequate conditions will be given on the parameters λ1, λ2, 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].