Existence of Solutions for Multi-Points Fractional Evolution Equations

In this paper we study an impulsive fractional evolution equation with nonlinear boundary conditions. Sufficient conditions for the existence and uniqueness of solutions are established. To illustrate our results, an example is presented

New integral results using Pólya-Szegö inequality

In this paper, we use the Riemann-Liouville fractional integral to present recent integral results using new inequalities of Pólya-Szegö type

Some Fractional Variational Problems Involving Caputo Derivatives

In this paper, we study some fractional variational problems with functionals that involve some unknown functions and their Caputo derivatives. We also consider Caputo iso-perimetric problems. Generalized fractional Euler-Lagrange equations for the problems are presented. Furthermore, we study the optimality conditions for functionals depending on the unknown functions and the optimal time T. In addition, some examples are discussed

Integral Inequalities and Differential Equations via Fractional Calculus

In this chapter, fractional calculus is used to develop some results on integral inequalities and differential equations. We develop some results related to the Hermite-Hadamard inequality. Then, we establish other integral results related to the Minkowski inequality. We continue to present our results by establishing new classes of fractional integral inequalities using a family of positive functions; these classes of inequalities can be considered as generalizations of order n for some other classical/fractional integral results published recently. As applications on inequalities, we generate new lower bounds estimating the fractional expectations and variances for the beta random variable. Some classical covariance identities, which correspond to the classical case, are generalised for any α ≥ 1 , β ≥ 1 . For the part of differential equations, we present a contribution that allow us to develop a class of fractional chaotic electrical circuit. We prove recent results for the existence and uniqueness of solutions for a class of Langevin-type equation. Then, by establishing some sufficient conditions, another result for the existence of at least one solution is also discussed

New classes of integral inequalities of fractional order

In this paper, the Riemann-Liouville fractional operator is used to generate new classes of integral inequalities using a family of n positive functions, (n ∈ N∗). For our results, some interesting classical inequalities can be deduced as some special cases

NEW EXISTENCE AND UNIQUENESS RESULTS FOR HIGH DIMENSIONAL FRACTIONAL DIFFERENTIAL SYSTEMS

In this paper using Caputo fractional derivative approach, wepresent recent results on the existence and uniqueness of solutions for

The foam drainage equation with time- and space-fractional derivatives solved by the Adomian method

In this paper, by introducing the fractional derivative in the sense of Caputo, we apply the Adomian decomposition method for the foam drainage equation with time- and space-fractional derivative. As a result, numerical solutions are obtained in a form of rapidly convergent series with easily computable components

A THREE FRACTIONAL ORDER JERK EQUATION WITH ANTI PERIODIC CONDITIONS

We study a new Jerk equation involving three fractional derivatives and anti periodic conditions. By Banach contraction principle, we present an existence and uniqueness result for the considered problem. Utilizing Krasnoselskii fixed point theorem we prove another existence result governing at least one solution. We provide an illustrative example to claim our established results. At the end, an approximation for Caputo derivative is proposed and some chaotic behaviours are discussed by means of the Runge Kutta 4th order method

New results for a weighted nonlinear system of fractional integro-differential equations

This paper studies the existence of solutions for a weighted systemof nonlinear fractional integro-dierential equations. New existence and uniqueness results are established using Banach xed point theorem. Other existence results are obtained using Schaefer xed point theorem. Some concrete examples are also presented to illustrate the possible application of the established analytical results

New W−W-weighted concepts for continuous random variables with applications

New concepts on fractional probability theory are introduced and some inequalities for the fractional $w-$weighted expectation and the fractional $w-$weighted variance of continuous random variables are obtained. Other fractional results related to the two orders-fractional $w-$% weighted moment are also established. Some recent results on integral inequality theory can be deduced as some special cases. At the end, some applications on the uniform random variable are given