When I talk about these prayers I mean prayers that are offered to God individually, only about your personal issues and may be your family. Mostly these prayers are private and often made in private or solitary places. When we talk about these prayers, Jesus set the best examples. From Gospels we find Jesus from time to time leaving His disciples to a solitary place to talk to God. The Bible says;
Mar 1:35 And in the morning, rising up a great while before day, he went out, and departed into a solitary place, and there prayed.
Jesus had a habit of leaving his disciple to pray alone in the presence of God. But why would Jesus go alone instead of going together with His disciples? Jesus had a very high burden of His call that no one else could have solved and understood apart from His father who sent Him to redeem Humanity hence only needed to talk with His father alone. There were also issues about His own disciples that He foresaw like betrayal, denial and rejection that they would show toward Him. Jesus knew these and He needed not to say or pray for it in public or during co-operate prayers, He needed to pray for it privately to the father.
Mar 14:32 And they came to a place which was named Gethsemane: and he saith to his disciples, Sit ye here, while I shall pray. 33 And he taketh with him Peter and James and John, and began to be sore amazed, and to be very heavy; 34 And saith unto them, My soul is exceeding sorrowful unto death: tarry ye here, and watch. 35 And he went forward a little, and fell on the ground, and prayed that, if it were possible, the hour might pass from him. 36 And he said, Abba, Father, all things are possible unto thee; take away this cup from me: nevertheless not what I will, but what thou wilt. 37 And he cometh, and findeth them sleeping, and saith unto Peter, Simon, sleepest thou? couldest not thou watch one hour? 38 Watch ye and pray, lest ye enter into temptation. The spirit truly is ready, but the flesh is weak. 39 And again he went away, and prayed, and spake the same words. 40 And when he returned, he found them asleep again, (for their eyes were heavy,) neither wist they what to answer him. 41 And he cometh the third time, and saith unto them, Sleep on now, and take your rest: it is enough, the hour is come; behold, the Son of man is betrayed into the hands of sinners. 42 Rise up, let us go; lo, he that betrayeth me is at hand.
From the above verses, Jesus had a lot of pain and a deep sorrow especially knowing that His own disciples like Peter and Judas would betray Him. He could not have co-operated with the same betrayers to pray against betray since they were the source and because He knew that this must happen for the prophesy to be true , He needed not to pray together with them over this issue necessitating for personal prayers. Jesus teaching about prayers said;
Mat 6:6 But thou, when thou prayest, enter into thy closet, and when thou hast shut thy door, pray to thy Father which is in secret; and thy Father which seeth in secret shall reward thee openly.
Brethren, there some matters or prayer needs that need not to be prayed publicly, they need you to go to your private, power or upper room that is secluded and in a solitary place.