We establish the existence and uniqueness of an attractive fractional coupled system. Such a system has applications in biological populations of cells. We confirm that the fractional system under consideration admits a global solution in the Sobolev space. The solution is shown to be unique. The technique is founded on analytic method of the fixed point theory and the fractional differential o...

In this paper, we study a coupled fully hybrid system of (k,Φ)–Hilfer fractional differential equations equipped with non-symmetric (k,Φ)–Riemann-Liouville (RL) integral conditions. To prove the existence and uniqueness results, use Krasnoselskii Perov fixed-point theorems Lipschitzian matrix in context generalized Banach space (GBS). Moreover, Ulam–Hyers (UH) stability solutions is discussed b...

New properties of the first‐order Riemann–Liouville fractional integrals are proved and derivatives for equivalence class functions in analyzed. Solutions, normal solutions, generalized solutions initial value problems (IVPs) nonlinear differential equations (FDEs) with fraction introduced. The equivalences between FDEs corresponding (Volterra) integral established based on solutions. results e...

The method ot atomic decomposition of Besov and Lizorkin-Triebel function spaces is combined with basic ideas from the theory of singular integral operators and applied to the study of fractional integral and diierential operators (FIDO), of which the Riesz potential is considered in detail as a model example. The main new results are: characterization of the Riesz potential by an innnite-dimen...

In this paper, we investigate the existence and nonexistence of positive solutions for a system Riemann–Liouville fractional differential equations with r-Laplacian operators, subject to nonlocal uncoupled boundary conditions that contain Riemann–Stieltjes integrals, various derivatives parameters. We first change unknown functions such new have no parameters, then, by using corresponding Green...

This article demonstrates some properties of the Riemann-Liouville (R-L) fractional integral operator like acting, continuity, and boundedness in Orlicz spaces L?. We apply these results to examine solvability quadratic equation order Because distinctive continuity conditions operators spaces, we look for our concern three situations when generating N-functions fulfill ??, ?2, or ?3-conditions....

This study establishes the existence and stability of solutions for a general class Riemann–Liouville (RL) fractional differential equations (FDEs) with variable order finite delay. Our findings are confirmed by fixed-point theorems (FPTs) from available literature. We transform RL FDE to alternate integral structure, then use classical FPTs, results studied Hyers–Ulam is established help stand...

Symmetry is a fascinating property of numerous mathematical notions. In analysis function f:[a,b]→R symmetric about a+b2 satisfies the equation f(a+b−x)=f(x). this paper, we investigate relationship unified Mittag–Leffler with some known special functions. We have obtained integral transforms in terms Wright generalized function. also established recurrence relation along another important resu...

We state, prove, and discuss new general inequality for convex and increasing functions. As a special case of that general result, we obtain new fractional inequalities involving fractional integrals and derivatives of Riemann-Liouville type. Consequently, we get the inequality of H. G. Hardy from 1918. We also obtain new results involving fractional derivatives of Canavati and Caputo types as ...

This paper addresses the problems of stability a nabla discrete distributed-order dynamical system (NDDS). Firstly, based on proposed generalized definition integral, some related definitions calculus are given. Then, several useful inequalities in sense fractional-order difference extended to cases. Meanwhile, basis and Lyapunov direct method, sufficient conditions guaranteeing asymptotic orig...