The Cauchy problems for q-difference equations with the Caputo fractional derivatives
Shaimardan S. Tokmagambetov N.S. Temirkhanova A.M.
31 March 2022al-Farabi Kazakh State National University
KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2022#113Issue 143 - 57 pp.
The fractional differential equations play important roles due to their numerous applications and also for the important role they play not only in mathematics but also in other sciences. In the present research work, we build up the explicit solutions to linear fractional q-differential equations with the q-Caputo fractional derivative of real order α > 0. To speak more precisely, we will achieve our main results we use that this Cauchy type q-fractional problem is equivalent to a corresponding Volterra q-integral equation. After that, by using the method of successive approximations is applied to solve the Volterra q-integral equation we construct the the explicit solutions to linear fractional q-differential equations. In the same way we have the more general homogeneous fractional q-differential equation with the Caputo fractional q-derivative of real order α > 0 and we give other The (Mittag-Leffler) q-function. Finally, some examples are presented to illustrate our main results in cases where we can even give concrete formulas for these explicit solutions.
Caputo fractional derivatives , Cauchy type q-fractional problem , existence , fractional calculus , fractional derivative , q-calculus , q-derivative , uniqueness
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L.N. Gumilyev Eurasian National University, Nur-Sultan, Kazakhstan
Karaganda Buketov University, Karaganda, Kazakhstan
L.N. Gumilyev Eurasian National University
Karaganda Buketov University
10 лет помогаем публиковать статьи Международный издатель
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