This paper investigates the existence of solutions for fractional-order neutral impulsive differential inclusions with nonlocal conditions. Utilizing the fractional calculus and fixed point theorem for multivalued maps, new sufficient conditions are derived for ensuring the existence of solutions. The obtained results improve and generalize some existed results. Finally, an illustrative example...

This paper proposes a novel method for controlling the convergence rate of a particle swarm optimization algorithm using fractional calculus (FC) concepts. The optimization is tested for several wellknown functions and the relationship between the fractional order velocity and the convergence of the algorithm is observed. The FC demonstrates a potential for interpreting evolution of the algorit...

In this research work, time-delay adaptive synchronization and anti-synchronization of chaotic fractional order systems are analyzed via the Caputo derivative, prob-lem variable is solved by using PID control law, laws variable-order frac-tional calculus, a law deduced from Lyapunov’s theory extended to calculus. two important problems in area: The first problem described which deals with syn-c...

‎‎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...

Differential and integral calculus belongs to basic courses of mathematics and everybody understands geometrical and physical meaning of derivative or integral. But, hardly anybody can imagine for example derivative of order 1/2 or even of non-rational order. The branch of mathematics which generalizes calculus to non-integer case is known under the term “fractional calculs” although this name ...

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...

Correspondence: [email protected] Department of Mathematics, Faculty of Science, Guelma University Guelma, Algeria Abstract In this article, sufficient conditions for the existence result of quasilinear multi-delay integro-differential equations of fractional orders with nonlocal impulsive conditions in Banach spaces have been presented using fractional calculus, resolvent operators, and ...

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing ...

fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. therefore, a reliable and efficient technique as a solution is regarded.this paper develops approximate solutions for boundary value problems ofdifferential equations with non-integer order by using the shannon waveletbases. wavelet bases have d...