The authors investigate the existence of solutions to a class boundary value problems for fractional q-difference equations in Banach space that involves q-derivative Caputo type and nonlinear integral conditions. Their result is based on Mönch’s fixed point theorem technique measures noncompactness. This approach has proved be an interesting useful studying such problems. Some basic concepts f...

Abstract Fractional calculus operators play a very important role in generalizing concepts of used diverse fields science. In this paper, we use Riemann–Liouville fractional integrals to establish generalized identities, which are further applied obtain midpoint and trapezoidal inequalities for convex function with respect strictly monotone function. These reproduce convex, harmonic p -convex, ...

The aim of this paper is to establish the existence of solutions of boundary value problems of nonlinear fractional integro-differential equations involving Caputo fractional derivative by using the techniques such as fractional calculus, H"{o}lder inequality, Krasnoselskii's fixed point theorem and nonlinear alternative of Leray-Schauder type. Examples are exhibited to illustrate the main resu...

Recently, many papers in the theory of univalent functions have been devoted to mapping and characterization properties of various linear integral or integro-differential operators in the class S (of normalized analytic and univalent functions in the open unit disk U), and in its subclasses (as the classes S∗ of the starlike functions and K of the convex functions in U). Among these operators, ...

Our goal in this article is to use ideas from symmetric q-calculus operator theory the study of meromorphic functions on punctured unit disc and propose a novel q-difference for these functions. A few additional classes are then defined light new operator. We prove many useful conclusions regarding newly constructed functions, such as convolution, subordination features, integral representation...

The principle of local gauge invariance is applied to fractional wave equations and the interaction term is determined up to order o(ḡ) in the coupling constant ḡ. As a first application, based on the RiemannLiouville fractional derivative definition, the fractional Zeeman effect is used to reproduce the baryon spectrum accurately. The transformation properties of the non relativistic fractiona...

Given a weighted ℓ 2 space with weights associated an entire function, we consider pairs of shift operators, whose commutators are diagonal when considered as operators over general Fock space. We establish calculus for the algebra these and apply it to case Gelfond–Leontiev derivatives. This class includes many known examples, such classic fractional derivatives Dunkl operators. allows us fram...

— This paper is a contribution to the general program of embedding theories of dynamical systems. Following our previous work on the Stochastic embedding theory developed with S. Darses, we define the fractional embedding of differential operators and ordinary differential equations. We construct an operator combining in a symmetric way the left and right (Riemann-Liouville) fractional derivati...