*Correspondence: [email protected] 1School of Mathematics and Physics, China University of Geosciences, Lumo 388, Wuhan, 430074, China Full list of author information is available at the end of the article Abstract In this paper we start by giving a new definition of weak Caputo derivative in the sense of distributions, and we give a variational formulation to a fractional diffusion equa...

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. New construction of the generalized Taylor’s power series is obtained. Some applicat...

In this paper, some theorems of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using Caputo fractional derivatives. Under some constraints, we proved that the Caputo fractional derivative can be expressed in terms of the ordinary derivative. A new construction of the generalized Taylor’s power series is obtained. Some applic...

In this paper, we introduce a new class of functions which are analytic and univalent with negative coefficients defined by using certain fractional operators described in the Caputo sense. Characterization property, the results on modified Hadamard product and integral transforms are discussed. Further, distortion theorem and radii of starlikeness and convexity are also determined here. Resume...

Right Caputo fractional ∥·∥p-Landau type inequalities, p ∈ (1,∞] are obtained with applications on R−.

This article discusses an iterative transformation method via fuzziness that mixtures the Laplace transform with method. Using Caputo derivative operator, proposed technique demonstrates inherent reliability of fractional fuzzy biological population equations initial conditions. The obtained results to are more general and apply a broad variety problems. A parametric description solutions is by...

Here we study the univariate fuzzy fractional quantitative approximation of real valued functions on a compact interval by quasi-interpolation arctangent-algebraic-Gudermannian-generalized symmetrical activation function relied neural network operators. These approximations are derived establishing Jackson type inequalities involving moduli continuity right and left...

In this note, we establish the sectorial property of the Caputo fractional derivative operator of order α ∈ (1, 2) with a zero Dirichlet boundary condition.

We study the properties of fractional differentiation with respect to the reflection symmetry in a finite interval. The representation and integration formulae are derived for symmetric and anti-symmetric fractional derivatives, both of the Riemann-Liouville and Caputo type. The action dependent on the left-sided Caputo derivatives of orders in the range (1,2) is considered and we derive the Eu...

Fractional Differential inclusions, the multivalued version of fractional differential equations, yellow play a vital role in various fields applied sciences. In present article, class q-rung orthopair fuzzy (q-ROF) set valued mappings along with q-ROF upper/lower semi-continuity have been introduced. Based on these ideas, existence theorems for numerical solution distinct inclusions achieved h...