Please see my note book http://mbed.org/users/kenjiArai/notebook/freertos-on-mbed-board-with-mbed-cloud-ide--never-/

This is too old.
Below is another FreeRTOS on mbed.
http://developer.mbed.org/users/rgrover1/code/FreeRTOS/
I don't know it works well or not.
I have not evaluated it.

Revision:
0:d4960fcea8ff
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/FreeRTOS/Source/portable/MemMang/heap_1.c	Sat Jan 01 11:17:45 2011 +0000
@@ -0,0 +1,153 @@
+/*
+    FreeRTOS V6.0.3 - Copyright (C) 2010 Real Time Engineers Ltd.
+
+    ***************************************************************************
+    *                                                                         *
+    * If you are:                                                             *
+    *                                                                         *
+    *    + New to FreeRTOS,                                                   *
+    *    + Wanting to learn FreeRTOS or multitasking in general quickly       *
+    *    + Looking for basic training,                                        *
+    *    + Wanting to improve your FreeRTOS skills and productivity           *
+    *                                                                         *
+    * then take a look at the FreeRTOS eBook                                  *
+    *                                                                         *
+    *        "Using the FreeRTOS Real Time Kernel - a Practical Guide"        *
+    *                  http://www.FreeRTOS.org/Documentation                  *
+    *                                                                         *
+    * A pdf reference manual is also available.  Both are usually delivered   *
+    * to your inbox within 20 minutes to two hours when purchased between 8am *
+    * and 8pm GMT (although please allow up to 24 hours in case of            *
+    * exceptional circumstances).  Thank you for your support!                *
+    *                                                                         *
+    ***************************************************************************
+
+    This file is part of the FreeRTOS distribution.
+
+    FreeRTOS is free software; you can redistribute it and/or modify it under
+    the terms of the GNU General Public License (version 2) as published by the
+    Free Software Foundation AND MODIFIED BY the FreeRTOS exception.
+    ***NOTE*** The exception to the GPL is included to allow you to distribute
+    a combined work that includes FreeRTOS without being obliged to provide the
+    source code for proprietary components outside of the FreeRTOS kernel.
+    FreeRTOS is distributed in the hope that it will be useful, but WITHOUT
+    ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+    FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for
+    more details. You should have received a copy of the GNU General Public 
+    License and the FreeRTOS license exception along with FreeRTOS; if not it 
+    can be viewed here: http://www.freertos.org/a00114.html and also obtained 
+    by writing to Richard Barry, contact details for whom are available on the
+    FreeRTOS WEB site.
+
+    1 tab == 4 spaces!
+
+    http://www.FreeRTOS.org - Documentation, latest information, license and
+    contact details.
+
+    http://www.SafeRTOS.com - A version that is certified for use in safety
+    critical systems.
+
+    http://www.OpenRTOS.com - Commercial support, development, porting,
+    licensing and training services.
+*/
+
+
+/*
+ * The simplest possible implementation of pvPortMalloc().  Note that this
+ * implementation does NOT allow allocated memory to be freed again.
+ *
+ * See heap_2.c and heap_3.c for alternative implementations, and the memory
+ * management pages of http://www.FreeRTOS.org for more information.
+ */
+
+#include <stdlib.h>
+
+/* Defining MPU_WRAPPERS_INCLUDED_FROM_API_FILE prevents task.h from redefining
+all the API functions to use the MPU wrappers.  That should only be done when
+task.h is included from an application file. */
+#define MPU_WRAPPERS_INCLUDED_FROM_API_FILE
+
+#include "FreeRTOS.h"
+#include "task.h"
+
+#undef MPU_WRAPPERS_INCLUDED_FROM_API_FILE
+
+/* Allocate the memory for the heap.  The struct is used to force byte
+alignment without using any non-portable code. */
+static union xRTOS_HEAP
+{
+    #if portBYTE_ALIGNMENT == 8
+        volatile portDOUBLE dDummy;
+    #else
+        volatile unsigned long ulDummy;
+    #endif    
+    unsigned char ucHeap[ configTOTAL_HEAP_SIZE ];
+} xHeap;
+
+static size_t xNextFreeByte = ( size_t ) 0;
+/*-----------------------------------------------------------*/
+
+void *pvPortMalloc( size_t xWantedSize )
+{
+void *pvReturn = NULL; 
+
+    /* Ensure that blocks are always aligned to the required number of bytes. */
+    #if portBYTE_ALIGNMENT != 1
+        if( xWantedSize & portBYTE_ALIGNMENT_MASK )
+        {
+            /* Byte alignment required. */
+            xWantedSize += ( portBYTE_ALIGNMENT - ( xWantedSize & portBYTE_ALIGNMENT_MASK ) );
+        }
+    #endif
+
+    vTaskSuspendAll();
+    {
+        /* Check there is enough room left for the allocation. */
+        if( ( ( xNextFreeByte + xWantedSize ) < configTOTAL_HEAP_SIZE ) &&
+            ( ( xNextFreeByte + xWantedSize ) > xNextFreeByte )    )/* Check for overflow. */
+        {
+            /* Return the next free byte then increment the index past this
+            block. */
+            pvReturn = &( xHeap.ucHeap[ xNextFreeByte ] );
+            xNextFreeByte += xWantedSize;            
+        }    
+    }
+    xTaskResumeAll();
+    
+    #if( configUSE_MALLOC_FAILED_HOOK == 1 )
+    {
+        if( pvReturn == NULL )
+        {
+            extern void vApplicationMallocFailedHook( void );
+            vApplicationMallocFailedHook();
+        }
+    }
+    #endif    
+
+    return pvReturn;
+}
+/*-----------------------------------------------------------*/
+
+void vPortFree( void *pv )
+{
+    /* Memory cannot be freed using this scheme.  See heap_2.c and heap_3.c 
+    for alternative implementations, and the memory management pages of 
+    http://www.FreeRTOS.org for more information. */
+    ( void ) pv;
+}
+/*-----------------------------------------------------------*/
+
+void vPortInitialiseBlocks( void )
+{
+    /* Only required when static memory is not cleared. */
+    xNextFreeByte = ( size_t ) 0;
+}
+/*-----------------------------------------------------------*/
+
+size_t xPortGetFreeHeapSize( void )
+{
+    return ( configTOTAL_HEAP_SIZE - xNextFreeByte );
+}
+
+
+