Abstract We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces functions defined on $${\mathbb {R}}$$ R , we define operators by means a functional calculus using the Fourier transform. Main tools are extrapolation- interpolation...

This paper establishes some closed formulas for RiemannLiouville impulsive fractional integral calculus and also for RiemannLiouville and Caputo impulsive fractional derivatives. Keywords—RimannLiouville fractional calculus, Caputo fractional derivative, Dirac delta, Distributional derivatives, Highorder distributional derivatives.

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

the aim of this paper is to present a new numerical method for solving the bagley-torvik equation. this equation has an important role in fractional calculus. the fractional derivatives are described based on the caputo sense. some properties of the sinc functions required for our subsequentdevelopment are given and are utilized to reduce the computation of solution of the bagley-torvik equatio...

Integration by parts plays a crucial role in mathematical analysis, e.g., during the proof of necessary optimality conditions calculus variations and optimal control. Motivated this fact, we construct new, right-weighted generalized fractional derivative Riemann-Liouville sense with its associated integral for recently introduced weighted Mittag-Leffler kernel. We rewrite these operators equiva...

Abstract The realization of fractional quantum chemistry is presented. Adopting the integro‐differential operators calculus arbitrary‐order, we develop a general framework for description nonlocal effects in complex electronic environments. After brief overview historical and fundamental aspects various classes Schrödinger equations are discussed pertinent controversies open problems around the...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...

A special function is a that typically entitled after an early scientist who studied its features and has specific application in mathematical physics or another area of mathematics. There are few significant examples, including the hypergeometric unique species. These types functions generalized by fractional calculus, fractal, q-calculus, (q,p)-calculus k-calculus. By engaging notion q-fracti...