Assalamu alaikum brothers and sisters.
Lately I've been trying to memorize Quran and sometimes I just start to forget some ayat, is there any dua to help me remember it. And please remember me in dua, I really want to do this.
Dua'a for Memory and Speech
If one fails to remember an event or written text or spoken words, according to Imam Jafar bin Muhammad al Sadiq one should put the right hand on the forehad and recite:
INNEE AS-ALUKA YAA MUD'AKKIRAL KHAYRI WA FAA-ILAHOO WAL AAMIRA BIHEE AN TUS'ALLIYA A'LAA MUH'AMMADIN WA AALI MUH'AMMADIN WA TUD'AKKIRANEE MAA ANSAANEEHISH SHAYT'AAN
I beseech You, O He who reminds about doing good, does good and commands to do good. Send blessings on Muhammed and the family of Muhammed and let me remember what shaytan makes me forget.
According to Imam Ali ibn abi Talib to retain in memory whatever one listens or reads, recite the following dua'a after every obligatory salat.
In the name of Allah the most kind the most merciful. Glory be to Him who does not treat the citizens of His kingdom unjustly. Glory be to Him who does not let the torment and pain come suddenly upon mankind. Glory be to the compassionate the merciful. O Allah, fill my heart with true enlightenment, wisdom, understanding and knowledge. Surely you are able to do all things. SUBH'AANA MAN LAA YA-TADEE AA'LAA AHLI MAMLAKATIHEE SUBH'AANA MAN LAA YAAKHUD'U AHLAL ARZ'I BILWAANIL A'D'AABI SUBH'AANAR RA-OOFIR RAH'EEMI ALLAAHUMMAJ-A'L LEE FEE QALBEE NOORAN WA BAS'ARAN WA FAHMAN WA I'LMAN INNAKA A'LAA KULLI SHAY-IN QADEER
Recite the following dua'a 7 times after obligatory salat to increase knowledge
RABBI ZIDNEE I'LMAA
To learn the holy Quran by heart (or remember its important verses) recite the following dua'a by Imam Ali ibn abi Talib written in Sahifa Alawiyyah
O Allah have mercy on me to be able to leave disobeying you till I am alive. Show mercy on me by not imposing a troublesome and difficult task on me. Make me do good deeds that please you. Make me learn your book by heart, just like you have taught me.Give me the ability to recite it in a manner that pleases you. O Allah (through the quran) enlighten my wisdom, open the doors of understanding and liberate my heart. Loosen my tongue, let my body be active and give me strength for it. No one can help me save you. There is no god except you.
ALLAAHUMMAR-H'AMNEE BITARKIL MA-A'AS'EE ABDAN MAA ABQAYTANEE FAR-H'AMNEE MIN TAKALLUFI MAA LAA YUNEENEE WARZUQNEE H'USNAL MANZ'ARI FEEMAA YURZ'EEKA A'NNEE WAL-ZAM QALBEE H'IFZ'A KITAABIKA KAMAA A'LLAMTANEE WARZUQNEE AN ATLUWAHOO A'LAN NAH'WIL LAD'EE YURZ'EEKA A'NNEE ALLAAHUMMA NAWWIR BAS'AREE WASH-RAH BIHEE S'ADRE WA FARRU BIHEE QALBEE WA AT'LIQ BIHEE LISAAANEE WAS-TA-MIL BIHEE BADANEE WA QAWWINEE A'LAA D'AALIKA WA A-I'NNEE A'LAYHI INNAHOO LAA MU-E'ENA A'LAYHI ILLAA ANTA LAA ILAAHA ILLAA ANTA
DUA'A 14 Whoever writes surah Bani Israil with saffron, washes it with pure water and drinks it will grow in wisdom and have fluent speech.
DUA'A 15 To speak clearly and fluently recite surah al Jumu-ah a great deal, and to have a photographic memory learn surah al A-laa by heart.
Memory and Retention Ayatullah ‘Ali Qadhi al-Tabataba’i would advise one to recite Ayat al-Kursi [2:255-257] and Ma’udhatayn (Surat al-Falaq and Surat al-Nas) for strengthening one’s memory
Reciting regularly Salwaat on the holy prophet & his household is also a method to improve ones memory
Take 4 or 7 almonds and pray salwat then pray "Ya Zul Jallale wal Ikraam" 11times, again salwat then and blow ( breathe on the almonds with the breath of the Zikr as you recite it ) on the almonds and eat them first thing every morning, Inshallah it will help your memory
From Baqiyatus slaehat ( margins of Mafatih ) :-
It is reported in 'Makaarimul Akhlaq' from Imam Muhammad Baqir (a.s.) and Imam Sadiq (a.s.) that one should write on a clean vessel with safron the Chapter of Al-Hamd, Ayatul Kursi, the Chapters of Qadr, Yasin, Waqiah, Hashr, Mulk, Ikhlas, Falaq and Nas and should then wash them with Zamzam water, rain water or clean water and add in the water about two grams of 'kandaroo', fifty grams of sugar and fifty grams of honey. At night it should be kept under open sky on iron.
At the end of the night one should recite two rakaats in each of which after the recitation of the Chapter of Al-Hamd, the chapter of Ikhlas be recited fifty times.
On completion of the salaat, one should drink the water which is good and tested
The following dua’a was taught by the Holy Prophet (S.A.) to Imam Ali (A.S.), to be recited after every obligatory Salaat, for developing a flawless memory:
Glory be to Him who does not treat the citizens of His Kingdom unjustly and harshly, Glory be to Him who does not let torment and pain come suddenly upon mankind, Glory be to the Compassionate, the Merciful. O Allah fill my heart and mind with true enlightenment, discerning intelligence, quick understanding and knowledge, Verily Thou art able to do all things.
سُبْحانَ مَنْ لا يَعْتَدي عَلى أهْلِ مَمْلَكَتِهِ سُبْحانَ مَنْ لا يَأخُذُ اَهْلَ الاَْرْضِ بأَلْوانِ الْعَذابِ سُبْحانَ الرَّؤوُفِ الرَّحيمِ اَللّـهُمَّ اْجَعلْ لي في قَلْبى نُوراً وَبَصَراً وَفَهْماً وَعِلْماً اِنَّكَ عَلى كُلِّ شَي قَديرٌ . Proven Supplication for increasing memory ( Tohfatul Hashmiya)
Write on seven pieces of sugar and eat a piece everyday. Write on the first one:
فَتَعٰلَی اللهُ الْمَلِكُ الْحَقُّ.
Fataa’a’lallaahul malikul haqq
Supremely exalted is therefore Allah, the King, the Truth,
and eat it on Saturday, and on the second write:
وَ قُلْ رَّبِّ زِدْنِيْ عِلْمًا. Wa qur rabbi zidnee i’lmaa.
And say: O my Lord! Increase me in knowledge.
and eat it on Sunday, and on the third write:
لاَ تُحَرِّكْ بِهِ، لِسَانَكَ.
Laa tuh’arrik-bihi lisaanak.
Do not move your tongue with it
and eat it on Monday, and on the fourth piece write
إِنَّ عَلَيْنَا جَمْعَهُ وَ قُرْأَنَهُ.
Inna a’lainaa jam-a’hu wa qur-aanah.
Surely on Us (devolves) the collecting of it and the reciting of it.
and eat it on Tuesday, and on the fifth piece write:
فَإِذَا قَرَأَنَهُ فَاتَّبِعْ قُرْأَنَهُ.
Fa-idhaa qaraa-nahu fattabi’ qur-aanah.
Therefore when We have recited it, follow its recitation.
and eat it on Wednesday, and on the sixth piece write:
سَنُقْرِئُكَ فَلاَ تَنْسٰى.
Sanuqri-uka falaa tansaa.
We will make you recite so you shall not forget,
and eat it on Thursday, and on the seventh piece write:
إنَّهُ يَعْلَمُ الْجَهْرَ وَ مَا يَخْفٰی.
Innahu ya’lamul jahra wa maa yakhfaa.
Surely He knows the manifest, and what is hidden.
and eat it on Friday.
Memorization would became easy for one who does this for seven days, and his tongue would become eloquent and his memory will increase.
Another Supplication for Memory
The Prophet (s.a.w.s.) said to Ali (a.s.): If you intend that you retain all that you hear, then recite the following after every ritual prayer:
سُبْحَانَ مَنْ لاَ يَعْتَدِىْ عَلٰی اَهْلِ مَمْلَكَتِهِ، سُبْحَانَ مَنْ لاَّ يَاْخُذُ أَهْلَ اْلاَرْضِ بِأَلْوَانِ الْعَذَابِ، سُبْحَانَ الرَّؤُفُ الرَّحِيْمُ، اَللَّهُمَّ اجْعَلْ فِیْ قَلْبِیْ نُوْرًا وَ بَصَرًا وَ فَهْمًا وَ عِلْمًا، إِنَّكَ عَلٰی كُلِّ شَیْءٍ قَدِيْرٌ.
Sub-h’aana mallaa ya’tadee a’laa ahli mamlikatih. Sub-h’aana mallaa yaa-khudhu ahlal arz”i bi-alwaanil adhaab. Sub-h’aanar ra-oofur rah’eem. Allaahummaj-a’l fee qalbee nooranw wa bas’araa. Wa fahimanw wa i’lmaa. Innaka a’laa kulli shai-in qadeer.
Glory be to the One who does not oppress His subjects, Glory be to the One Who does not subject the people of the earth to various punishments, Glory be to the forgiving and the Merciful, O Allah, put in my heart a light and perception and understanding. Indeed You are powerful over all things.
 Surah Taha 20:114  Surah Taha 20:114  Surah Qiyamah 75:16  Surah Qiyamah 75:17  Surah Qiyamah 75:18  Surah Alaa 87:6  Surah Alaa 87:7  Tibb al-Aaimma, As-Sayyid Shubbar, Pg. 388