and Applied Analysis 3 Definition 2.2 see 15 . A cone K is called normal, if there exists a positive constant r such that f, g ∈ K and θ ≺ f ≺ g implies ‖f‖ ≤ r‖g‖, where θ denotes the zero element of K. Definition 2.3 see 16, 17 . Let f : a, b → R, and f ∈ L1 a, b . The left-sided RiemannLiouville fractional integral of f of order α is defined as I af x 1 Γ α ∫x a x − t α−1f t dt, α > 0, x ∈ a...

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

The present paper deals with the wavelet transform of fractional integral operator (the RiemannLiouville operators) on Boehmian spaces. By virtue of the existing relation between the wavelet transform and the Fourier transform, we obtained integrable Boehmians defined on the Boehmian space for the wavelet transform of fractional integrals.

In this paper, we discus the existence of solutions for RiemannLiouville fractional differential inclusions supplemented with ErdélyiKober fractional integral conditions. We apply endpoint theory, Krasnoselskii’s multi-valued fixed point theorem and Wegrzyk’s fixed point theorem for generalized contractions. For the illustration of our results, we include examples.

This paper presents improvements of some Opial-type inequalities involving the RiemannLiouville, Caputo and Canavati fractional derivatives, and presents some new Opial-type inequalities. Mathematics subject classification (2010): 26A33, 26D15.

approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. in this paper with central difference approximation and newton cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. three...

This article concerns a general fractional differential equation of order between 1 and 2. We consider the cases where the nonlinear term contains or does not contain other (lower order) fractional derivatives (of RiemannLiouville type). Moreover, the nonlinearity involves also a nonlinear non-local in time term. The case where this non-local term has a singular kernel is treated as well. It is...

In this paper, we consider some boundary value problems (BVP) for fractional order partial differential equations ‎(FPDE)‎ with non-local boundary conditions. The solutions of these problems are presented as series solutions analytically via modified Mittag-Leffler functions. These functions have been modified by authors such that their derivatives are invariant with respect to fractional deriv...

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where RiemannLiouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions ...

Abstract In this paper, the numerical method for solving Abel’s integral equations is presented. This method is based on fractional calculus. Also, Chebyshev polynomials are utilized to apply fractional properties for solving Abel’s integral equations of the first and second kind. The fractional operator is considered in the sense of RiemannLiouville. Although Abel’s integral equations as singu...