Sometimes we need to create indexes for some partitions. Oracle 11g provides this function. You can create local and global indexes on partial partitions.
Global partial index: only those partitions that need to be indexed will be indexed, and other partitions will not be created.
Local index: if index is turned on for table partition, index partition is available; otherwise, it is not available. You can override this behavior by specifying USABLE / UNUSABLE at the index or index partition level.
This function does not support unique index. full is the default mode.
The indexing clause can be specified at the level of a partition or sub partition.
The following example is taken from the official website

CREATE TABLE orders (
  order_id NUMBER(12),
  order_date DATE CONSTRAINT order_date_nn NOT NULL,
  order_mode VARCHAR2(8),
  customer_id NUMBER(6) CONSTRAINT order_customer_id_nn NOT NULL,
  order_status NUMBER(2),
  order_total NUMBER(8,2),
  sales_rep_id NUMBER(6),
  promotion_id NUMBER(6),
  CONSTRAINT order_mode_lov CHECK (order_mode in ('direct','online')),
  CONSTRAINT order_total_min CHECK (order_total >= 0))
   INDEXING OFF
   PARTITION BY RANGE (ORDER_DATE)
   (PARTITION ord_p1 VALUES LESS THAN (TO_DATE('01-MAR-1999','DD-MON-YYYY')) 
     INDEXING ON,
   PARTITION ord_p2 VALUES LESS THAN (TO_DATE('01-JUL-1999','DD-MON-YYYY')) 
     INDEXING OFF,
   PARTITION ord_p3 VALUES LESS THAN (TO_DATE('01-OCT-1999','DD-MON-YYYY')) 
     INDEXING ON,
   PARTITION ord_p4 VALUES LESS THAN (TO_DATE('01-MAR-2000','DD-MON-YYYY')),
   PARTITION ord_p5 VALUES LESS THAN (TO_DATE('01-MAR-2010','DD-MON-YYYY')));

//Create global index
CREATE INDEX ORDERS_ORDER_TOTAL_GIDX ON ORDERS (ORDER_TOTAL)
   GLOBAL INDEXING PARTIAL;
SQL>  select index_name,index_type,partitioned,orphaned_entries,indexing from user_indexes;

INDEX_NAME                     INDEX_TYPE                  PAR ORP INDEXIN
------------------------------ --------------------------- --- --- -------
PK_DEPT                        NORMAL                      NO  NO  FULL
PK_EMP                         NORMAL                      NO  NO  FULL
ORDERS_ORDER_TOTAL_GIDX        NORMAL                      NO  NO  PARTIAL
SQL>  select * from user_ind_partitions ;

no rows selected
//Next, create the local partition index
create index idx_orders_local on orders(order_date) local;
select index_name,partition_name,status from user_ind_partitions ;
SQL>  select index_name,partition_name,status from user_ind_partitions ;

INDEX_NAME           PARTITION_NAME       STATUS
-------------------- -------------------- --------
IDX_ORDERS_LOCAL     ORD_P1               USABLE
IDX_ORDERS_LOCAL     ORD_P2               USABLE
IDX_ORDERS_LOCAL     ORD_P3               USABLE
IDX_ORDERS_LOCAL     ORD_P4               USABLE
IDX_ORDERS_LOCAL     ORD_P5               USABLE


SQL> create index idx_orders_local on orders(order_date) local indexing partial;

Index created.

SQL>  select index_name,partition_name,status from user_ind_partitions ;

INDEX_NAME           PARTITION_NAME       STATUS
-------------------- -------------------- --------
IDX_ORDERS_LOCAL     ORD_P1               USABLE
IDX_ORDERS_LOCAL     ORD_P2               UNUSABLE
IDX_ORDERS_LOCAL     ORD_P3               USABLE
IDX_ORDERS_LOCAL     ORD_P4               UNUSABLE
IDX_ORDERS_LOCAL     ORD_P5               UNUSABLE
//You can see that the local partition index only sets the state of the partition containing the indexing property to usable