We are concerned with the existence and nonexistence of positive solutions for the nonlinear fractional boundary value problem: D 0+u(t) + λa(t) f (u(t)) = 0, 0 < t < 1, u(0) = u ′ (0) = u(1) = 0, where 2 < α < 3 is a real number and D 0+ is the standard RiemannLiouville fractional derivative. Our analysis relies on Krasnoselskiis fixed point theorem of cone preserving operators. An example is ...

Based on the Riemann fractional derivative the Casimir operators and multipletts for the fractional extension of the rotation group SO(n) are calculated algebraically. The spectrum of the corresponding fractional rigid rotator is discussed. It is shown, that the rotational, vibrational and γ unstable limits of the standard geometric collective models are particular limits of this spectrum. A co...

In this study, the localfractional variational iterationmethod (LFVIM) and the localfractional series expansion method (LFSEM) are utilized to obtain approximate solutions for Korteweg-de Vries equation (KdVE) within local fractionalderivative operators (LFDOs). The efficiency of the considered methods is illustrated by some examples. The results reveal that the suggested algorithms are very ef...

Based on the Riemann fractional derivative the Casimir operators and multiplets for the fractional extension of the rotation group SO(n) are calculated algebraically. The spectrum of the corresponding fractional symmetric rigid rotor is discussed. It is shown, that the rotational, vibrational and γ-unstable limits of the standard geometric collective models are particular limits of this spectru...

The paper is concerned with existence of mild solution of evolution equation with Hilfer fractional derivative which generalized the famous Riemann–Liouville fractional derivative. By noncompact measure method, we obtain some sufficient conditions to ensure the existence of mild solution. Our results are new and more general to known results. Nowadays, fractional calculus receives increasing at...

This study introduces some remarks on generalized fractional integral and differential operators, which generalize familiar derivative with respect to a given function. We briefly explain how formulate representations of operators. Then, mainly, we propose predictor–corrector algorithm for the numerical simulation initial value problems involving Caputo-type derivatives another Numerical soluti...

A finite element scheme for an entirely fractional Allen–Cahn equation with non-smooth initial data is introduced and analyzed. In the proposed nonlocal model, Caputo in-time derivative Laplacian replace standard local operators. Piecewise linear elements convolution quadratures are basic tools involved in presented numerical method. Error analysis implementation issues addressed together neede...

Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...

Abstract In this paper, we first provide a short summary of the main properties so-called general fractional derivatives with Sonin kernels introduced so far. These are integro-differential operators defined as compositions order derivative and an integral operator convolution type. Depending on succession these operators, Riemann-Liouville Caputo types were studied. The objective paper is cons...

In this paper, a criterion for generating an analytic family of operators, which resolves linear equation solved with respect to the Dzhrbashyan–Nersesyan fractional derivative, via closed operator is obtained. The properties resolving families are investigated and applied prove existence unique solution corresponding initial value problem inhomogeneous derivative. A presented explicitly using ...