Fractional and operational calculus with generalized fractional derivative operators and Mittag–Leffler type functions

Analytic solutions of fractional integro-differential equations of Volterra type with variable coefficients

“…Some compositional properties with the generalized R-L fractional derivative operator and Hardy type inequality with generalized R-L fractional derivative operator were obtained in the recent papers [28,29]. Using the Laplace transformation method, several fractional differential equations with constant and variable coefficients, as well as some Volterra integrodifferential equations in the space of summable functions y(x) ∈ L(0, ∞), were solved, see e.g.…”

“…Using the Laplace transformation method, several fractional differential equations with constant and variable coefficients, as well as some Volterra integrodifferential equations in the space of summable functions y(x) ∈ L(0, ∞), were solved, see e.g. [28], [29]. An operational calculus of the Mikusinski type was introduced for the generalized R-L fractional derivative operator in [10] and it was used to solve the corresponding n-initial value problem for the general n-term linear fractional differential equation with constant coefficients with generalized R-L fractional derivatives of arbitrary orders and types.…”

Operational method for solving multi-term fractional differential equations with the generalized fractional derivatives

“…The concept of GRLFD has appeared in the theoretical modeling of broadband dielectric relaxation spectroscopy for glasses [5]. Some properties and applications of the GRLFD are given in [3,4,18,20,21,22]. Several authors (see [2,18,22] [2,18,22,23].…”

Uncertain Hermite-Hadamard inequality for functions with (s,m)-Godunova-Levin derivatives via fractional integral

“…For more information about its interesting history and wide applications, see [15,17,18,19,20]. According to the importance of account deficits, more attention has been attracted and a lot of quality researches in this branch of mathematical analysis have been carried out, (see [3,10,21] and the references therein). Anastassiou [1,2] proved the fuzzy Ostrowski's inequalities.…”