*Correspondence: [email protected] 1Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract This paper investigates a boundary value problem of Caputo type sequential fractional differential equations supplemented with nonlocal Riemann-Liouville f...

In this study, we present a new notion of nonlocal closed boundary conditions. Equipped with these conditions, discuss the existence solutions for mixed nonlinear differential equation involving right Caputo fractional derivative operator, and left Riemann–Liouville integral operators different orders. We apply decent fruitful approach fixed point theory to establish desired results. Examples a...

This paper considers the Riemann–Liouville fractional operator as a tool to reduce linear ordinary equations with variable coefficients to simpler problems, avoiding the singularities of the original equation. The main result is that this technique allow us to obtain an extension of the classical integral representation of the special functions related with the original differential equations. ...

We apply generalized operators of fractional integration involving Appell's function F 3(·) due to Marichev-Saigo-Maeda, to the product of the generalized Bessel function of the first kind due to Baricz. The results are expressed in terms of the multivariable generalized Lauricella functions. Corresponding assertions in terms of Saigo, Erdélyi-Kober, Riemann-Liouville, and Weyl type of fraction...

Simpson’s rule is a numerical method used for approximating the definite integral of function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire upper and lower bounds Simpson-type inequalities means Riemann–Liouville fractional operators. We also study special cases our main results. Furthermore, give some examples with graphs to illustrate This on first pap...

‎in this paper‎, ‎we study stability of fractional-order nonlinear dynamic systems by means of lyapunov‎ ‎method‎. ‎to examine the obtained results‎, ‎we employe the developed techniques on test examples‎.

In this paper, we derive a new extension of Hermite-Hadamard's inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appell's hypergeometric functions. These bounds can be viewed as new k-fractional estimations of trapezoidal a...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

The main goal of this paper is to describe the new version extended Bessel–Maitland function and discuss its special cases. Then, using aforementioned as their kernels, we develop generalized fractional integral differential operators. convergence boundedness newly operators compare them with existing such Saigo Riemann–Liouville are explored. transforms defined in terms Fox–Wright presented. A...