وجود الحلول الموجبة لمسائل القيم الحدودية لمعادلة تفاضلية لا خطية من الرتب الكسرية

الملخص EN

Recently boundary value problems for differential equations of non-integral order have studied in many papers ( see [1, 2] ).

Zaho etal [ 1 ] studied the following boundary value problem of fractional differential equations.

Where denotes the Rimann-Liouville fractional derivative equation of order.

By using the lower and upper solution method and fixed point theorem.

Liang and Zhang [3] studied the non-linear fractional differential boundary value problemWhere is a real number.

is the Rimann-Liouville fractional differential operator of order.

By means of fixed point theorems, they obtained results on the existence of positive solutions for boundary value problem of fractional differential equations.

In this paper, we deal with some existence of positive solution of the following non-linear fractional differential equation.

Where is a real number.

denotes Rimann-Liouville fractional derivative of order.

Our work based on Banach contraction mapping and Krasnoel'skii fixed point theorems to investigate the existence of positive solution.

Finally, we suggest studing the existence solutions for the following Integrodifferential equation with boundary value conditionsWhere H is a nonlinear integral operator given