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The aim of this paper is to study the existence and uniqueness of solutions for the boundary value problem for nonlinear implicit fractional differential equations involving standard Riemann-Liouville fractional derivative. Our results are based on the Banach's contraction mapping principal and Krasnoselskii's fixed point theorem. Finally, one illustrative example is given to demonstrate the obtained results.

In this paper, we study the existence and other properties of the solution of nonlinear mixed fractional integro-differential equations with constant coefficient. Also with the help of integral inequality of mixed type, we prove the continuous dependence of the solutions on the initial conditions.

Riccati differential equations are usually arises in many fields of applied science. In this paper, we suggest a new iterative method proposed by Daftardar-Gejji and Jafari to solve the Riccati differential equation. We use software Mathematic for computations. We discussed numerical examples to demonstrate the efficiency and the accuracy of the proposed Method.