The present paper deals with the study of a generalized Mittag-Leffler function and associated fractional operator. The operator has been discussed in the space of Lebesgue measurable functions. The composition with Riemann-Liouville fractional integration operator has been obtained.

In this paper, we investigate the existence and uniqueness of solution of the periodic boundary value problem for nonlinear impulsive fractional differential equation involving Riemann-Liouville fractional derivative by using Banach contraction principle.

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen’s inequality for differentiable convex functions. The main findings were effectively composed functions and their properties. results directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma modified Bessel functions, some applications acquired ob...

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using ...

We study dynamic minimization problems of the calculus of variations with Lagrangian functionals containing Riemann–Liouville fractional integrals, classical and Caputo fractional derivatives. Under assumptions of regularity, coercivity and convexity, we prove existence of solutions. AMS Subject Classifications: 26A33, 49J05.

In this paper, under some super- and sub-linear growth conditions, we study the existence of positive solutions for a high-order Riemann–Liouville type fractional integral boundary value problem involving derivatives. Our analysis methods are based on fixed point index nonsymmetric property Green function. Additionally, provide valid examples to illustrate our main results.

In this work we study fractional order Sumudu transform. In the development of the definition we use fractional analysis based on the modified Riemann Liouville derivative, then we name the fractional Sumudu transform. We also establish a relationship between fractional Laplace and Sumudu via duality with complex inversion formula for fractional Sumudu transform and apply new definition to solv...

Abstract In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo derivatives with initial integral conditions. Some new results on the existence uniqueness of solution for model are obtained as well Ulam stability solutions. Two examples provided to show applicability our results.

In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella functions, by using the extended Bessel due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform integral representations are obtained for these generalizations. Further, an extension Riemann-Liouville fractional deri...