We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.

In this paper, we deal with non-linear functional fractional differential equation with initial condition in 1 L space. We will study the existence, uniqueness and stability of the solution of fractional differential equation. Keywords: Fractional differential equation; Riemann Liouville Fractional derivative; Stability. ‫ال‬ ‫و‬ ‫الوجود‬ ‫نظريات‬ ‫وحدانية‬ ‫ار‬ ‫االستقر‬ ‫و‬ ‫ية‬ ‫الوظيفية‬ ‫الجزئية‬ ‫األولية‬ ‫القيمة‬ ‫مشكالت‬ ‫لبعض‬ ‫االحد‬ ‫عبد‬ ‫جوزيف‬ ‫مر‬ ‫شيماء‬ ‫اد‬ ‫كلية‬ ‫بية،‬ ‫التر‬ ‫جامعة‬ ‫دهوك‬ ‫البحث:‬ ‫استالم‬ ‫تاريخ‬ 21 / 10 / 2009 ‫البحث:‬ ‫قبول‬ ‫تاريخ‬ 11 / 04 / 2010 ‫الملخص‬ ‫ا‬ ‫م‬ ‫اة‬ ‫المطي‬ ‫ار‬ ‫الال‬ ‫ي‬ ‫اة‬ ‫ار‬ ‫الية‬ ‫ال‬ ‫ت‬ ‫الر‬ ‫تا‬ ‫الية‬ ‫التاال‬ ‫اادت‬ ‫المع‬ ‫إلى‬ ‫قنا‬ ‫تطر‬ ‫البحث‬ ‫هذا‬ ‫في‬ ‫اي‬ ‫ف‬ ‫اة‬ ‫اتتاايي‬ ‫اري‬ ‫ش‬ ‫الاضاء‬ 1 L ‫الوجود‬ ‫اسة‬ ‫در‬ ‫تمت‬ ‫يقا‬ ، ‫اة‬ ‫اليةر‬ ‫التااللية‬ ‫المعادت‬ ‫لحل‬ ‫اة‬ ‫ار‬ ‫اتستقر‬ ‫ي‬ ‫الوحاانية‬ ‫ي‬ . ‫المفتاحية:‬ ‫الكلمات‬ ‫التااللية‬ ‫المعادلة‬ ‫تل‬ ‫ر‬ ‫تا‬ ‫اة؛‬ ‫كةر‬ ‫مشتقة‬ Riemann Liouville ‫اية‬ ‫اتستقر‬ ، .

This paper presents a numerical method based on neural network, for solving the Lane-Emden equations singular initial value problems. The numerical solution is given for integer case and non integer case. The non integer case is taken in the sense of Riemann-Liouville operators.

In this study, by applying some fixed point theorems when ∈ ( − , ], the existence and uniqueness theorem for certain fractional differential equations with fractional boundary conditions is established. The theories are illustrated by examples.

<abstract><p>In this paper, we study the existence, uniqueness, and stability theorems of solutions for a differential equation of mixed Caputo-Riemann fractional derivatives with integral initial conditions in a Banach space. Our analysis is based on an application of the Shauder fixed point theorem with Ulam-Hyers and Ulam-Hyers-Rassias theorems. A couple of examples are presented to illustrate the obtained results.</p></abstract>