We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

*Correspondence: [email protected] Chung-Jen Junior College of Nursing, Health Sciences and Management, Dalin, 62241, Taiwan Abstract In this paper, we establish sufficient optimality conditions for the (weak) efficiency to multiobjective fractional programming problems involving generalized (F,α,ρ ,d)-V-type I functions. Using the optimality conditions, we also investigate a parametric-type dua...

‎In this paper we propose a method for computing approximations of solution of fuzzy fractional differential equations using fuzzy variational iteration method. Defining a fuzzy fractional derivative, we verify the utility of the method through two illustrative ‎examples.‎

In this paper we will prove certain Hadamard and Fejer-Hadamard inequalities for the functions whose nth derivatives are convex by using Caputo k-fractional derivatives. These results have some relationship with inequalities for Caputo fractional derivatives.

In this paper we present a review of the main theoretical results obtained up to now in bicriterion fractional programming with few exceptions related to general results for bicriteria problems. With respect to sequential methods, we limit ourselves to present computational approaches for linear fractional problems.

For 1 1 ( ) ( )∈! m m m x = x ,...,x , y = y ,...,y we put ≤ x y iff i i x y ≤ for each { } 1 2 ∈ i M = , ,...,m ; ≤ x y iff ≤ i i x y for each i M ∈ , with x y; x < y ≠ iff i i x < y for each i M ∈ . We write + ∈! m x iff 0 ≥ x . For an arbitrary vector n x∈! and a subset J of the index set { } 1 2 n , ,..., , we denote by J x the vector with components j x , j J ∈ . Let ( ) μ X , Γ, be a fini...

for any $k in mathbb{n}$, the $k$-subdivision of graph $g$ is a simple graph $g^{frac{1}{k}}$, which is constructed by replacing each edge of $g$ with a path of length $k$. in [moharram n. iradmusa, on colorings of graph fractional powers, discrete math., (310) 2010, no. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $g$ has been introduced as a fractional power of $g$, denoted by ...