Riemann-Liouville and Hadamard type generalized fractional differential equations

Fractional calculus is based on a very long history. Fractional differential and integration are generalization of integer order derivative and n -times integrals. These notions were originally proposed by Leibniz in the 17th century and then many mathematician worked on this subject like Euler, Lagrange, Abel, Liouville. In this work, which is consisted of four chapters, Riemann-Liouville and Hadamard type generalized fractional integral defined by (∫_0^t K_ρ^α (t,η)f(η)dη, α∈R/Z_0^- [J_ρ^α f](t)≔{ f(t), α=0 ∑_(i=1)^((-α))(A_((-α),i) (ρ))/t^((-α)ρ-i) (d/dt)^i f(t), α∈Z^- where α∈R,ρ∈R^+ and f:(0,∞)→R. In the first chapter of this work, a general knowledge about the fractional derivative. In the second chapter of this work, some basic definitions and theorems, necessary for this work, are given. In the third chapter, Riemann-Liouville and Hadamard type generalized fractional integral and derivative are defined and basic features are given, in the last chapter focused on solution of Riemann-Liouville and Hadamard type generalized fractional differential equations.