In this paper, we consider fractional differential equations with the new derivative involving a nonsingular kernel, namely, Caputo-Fabrizio derivative. Using successive approximation method, prove an extension of Picard-Lindelöf existence and uniqueness theorem for derivative, which gives set conditions, under initial value problem has unique solution.

The diagnosis of acromegaly is based on clinical features and biochemical criteria. While clinical suspicion is of extreme importance, laboratory evaluation is mandatory to establish the diagnosis. Growth hormone (GH) is secreted in a pulsatile pattern. Normal individuals have undetectable levels during most of the daytime period. In contrast, GH is always detectable in acromegalic patients, pr...

Recombinant human growth hormone (hGH) was given for 6 months or longer to 68 patients with GH deficiency, 6 with Turner's syndrome and 5 with achondroplasia, during 1986-1994 in a prospective study. The total weekly administered dose of GH was 0.6 u/kg. By random sampling, 29 of 68 GH deficient patients (42.6%) received twice weekly (2 iw) intramuscular (im) injections, 17 (25%) received ...

‎The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the ‎method.

The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...

This paper investigates the solvability, existence and uniqueness of solutions for a class of nonlinear fractional hybrid differential equations with Hilfer fractional derivative in a weighted normed space. The main result is proved by means of a fixed point theorem due to Dhage. An example to illustrate the results is included.

*Correspondence: [email protected] 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK Full list of author information is available at the end of the article Abstract We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fract...

<p>This article introduces some new straightforward and yet powerful formulas in the form of series solutions together with their residual errors for approximating Riemann-Liouville fractional derivative operator. These are derived by utilizing forthright computations, so-called weighted mean value theorem (WMVT). Undoubtedly, such will be extremely useful establishing approaches several ...

We study quantum corrections on four derivative term of vector multiplets in N = 2 supersymmetric Yang-Mills theory. We first show splitting of quantum correction on gauge neutral hypermultiplets from U(1) vector multiplets at four derivative order. We then revisit the non-renormalization theorem given by N. Seiberg and M. Dine and show the non-renormalization theorem in mixed (Coulomb plus Hig...