SOLVING A BOUNDARY VALUE PROBLEM FOR THE FIRST ORDER DIFFERENTIAL EQUATION INVOLVING THE PRABHAKAR OPERATOR
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Ushbu ishda Prabhakar kasr tartibli hosilasi qatnashgan birinchi tartibli xususiy hosilali differensial
tenglama to’g‘ri to‘rtburchakli sohada qaralgan. Bu tenglama uchun bir chegaraviy masalaning bir
qiymatli yechilishi o‘rganilgan. Bu masalaning yechimini topish uchun Riman usulidan foydalanilgan.
Riman funksiyasiga nisbatan yordamchi masala hosil qilingan. Yordamchi masalani Laplas
almashtirishi yordamida oddiy differensial tenglama uchun Koshi masalasiga olib kelingan va teskari
Laplas almashtirishini qo‘llab yordamchi masalaning yechim formulasi, ya’ni berilgan masalaning
Riman funksiyasi topilgan. So’ngra Riman metodidan foydalanib dastlabki masalaning yechimi
topilgan. Topilgan yechim masalaning shartlarini qanoatlantirishi uchun berilgan funksiyalarga
yetarli shartlar topilgan.
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