In this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional Cauchy problem with an integral initial condition in Banach spaces.

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

multi objective quadratic fractional programming (moqfp) problem involves optimization of several objective functions in the form of a ratio of numerator and denominator functions which involve both contains linear and quadratic forms with the assumption that the set of feasible solutions is a convex polyhedral with a nite number of extreme points and the denominator part of each of the object...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

In this note we consider a linear-fractional programming problem with equality linear constraints. Following Rohn, we define a generalized relative sensitivity coefficient measuring the sensitivity of the optimal value for a linear program and a linear-fractional minimization problem with respect to the perturbations in the problem data. By using an extension of Rohn’s result for the linear pro...

We consider an aggregation equation in Rn, n ≥ 2, with fractional dissipation, namely, ut + ∇ · (u∇K ∗ u) = −ν(−∆)γ/2u , where 0 ≤ γ ≤ 2 and K is a nonnegative decreasing radial kernel with a Lipschitz point at the origin, e.g. K(x) = e−|x|. We prove that for 0 ≤ γ < 1 the solutions develop blow-up in finite for a general class of initial data. In contrast we prove that for 1 < γ ≤ 2 the equati...

This paper presents a fractional mathematical model of a one-dimensional phase-change problem (Stefan problem) with a variable latent-heat (a power function of position). This model includes space–time fractional derivatives in the Caputo sense and time-dependent surface-heat flux. An approximate solution of this model is obtained by using the optimal homotopy asymptotic method to find the solu...

this paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. we show that it has at least one or two positive solutions. the main tool is krasnosel'skii fixed point theorem on cone and fixed point index theory.