[PDF] Top 20 New concepts of fractional quantum calculus and applications to impulsive fractional q difference equations
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New concepts of fractional quantum calculus and applications to impulsive fractional q difference equations
... In applications, as in constructing a q-Taylor formula or solving q-differential equations and inequalities of fractional order, it is interesting to allow nonzero lower limits of ... See full document
19
New concepts of fractional Hahn’s \(q,\omega \) derivative of Riemann–Liouville type and Caputo type and applications
... Hahn quantum variational calculus, while Malinowska and Martins [13] studied the generalized transversality conditions for the Hahn quantum vari- ational ...some concepts of fractional ... See full document
21
Nonlocal boundary value problems for impulsive fractional \(q {k}\) difference equations
... the q-derivative and q-integral were defined. New definitions of the Riemann-Liouville fractional q-integral and q-difference on an interval [a, b] were given, and their basic ... See full document
16
New applications of the variational iteration method from differential equations to q fractional difference equations
... In Sections and , we note that the integration by parts plays an important role and is often used in the derivation of the Lagrange multipliers in ordinary calculus. But in FC, the similar integration by parts ... See full document
16
Applications of quantum calculus on finite intervals to impulsive difference inclusions
... tum calculus. In recent years, the topic of q-calculus has attracted the attention of several researchers and a variety of new results can be found in the papers [–] and the refer- ences ... See full document
16
Quantum calculus on finite intervals and applications to impulsive difference equations
... Quantum calculus is the modern name for the investigation of calculus without ...The quantum calculus or q-calculus began with FH Jackson in the early twentieth century, ... See full document
19
On the oscillation of q fractional difference equations
... difference equations intuitively lead to developments in the direction of q-fractional calculus which deals with fractional deriva- tives and integrals with arbitrary order on the ... See full document
11
Existence results for impulsive fractional q-difference equations with anti-periodic boundary conditions
... The quantum calculus (calculus without limits or q-calculus) is concerned with differ- ence operators and allows one to deal with sets of nondifferentiable ...functions. Quantum ... See full document
14
New concepts of Hahn calculus and impulsive Hahn difference equations
... Many physical phenomena are described by equations involving nondifferentiable func- tions, e.g., generic trajectories of quantum mechanics []. Several different approaches to deal with nondifferentiable ... See full document
19
Existence and uniqueness of solutions for multi term fractional q integro differential equations via quantum calculus
... of fractional calculus and q-calculus are one of the significant branches in mathematical ...of q-difference equations was introduced by Jackson ...the q-difference equation ... See full document
20
A numerical approach for variable-order fractional unified chaotic systems with time-delay
... engineering applications, such as electrical engineering, informa- tion processing, secure ...in fractional- order systems is ...other fractional order chaotic systems have been introduced, such as ... See full document
15
Construction of Toeplitz matrices whose elements are the coefficients of univalent functions associated with Q-derivative operator
... Toeplitz matrices frequently arise in many application areas and have been attracted much attention in recent years. They arise in pure math- ematics: algebra, algebraic geometry, analysis, combinatorics, differen- tial ... See full document
7
On a new class of impulsive fractional evolution equations
... Remark . By applying the Laplace transform and probability density functions, Zhou and Jiao [, ] introduced the above definition of mild solutions for fractional evolution equations. For pioneering ... See full document
16
INTERNATIONAL JOURNAL OF ENGINEERING SCIENCES & MANAGEMENT NEW MM- FUNCTION AND FRACTIONAL CALCULUS Manoj Sharma
... a new function termed as New Mm- function has been ...of fractional integral equations in those ...the fractional integration and fractional differentiation of New Mm- ... See full document
5
Impulsive fractional quantum Hahn difference boundary value problems
... where ω > 0 is a fixed constant. The Hahn difference operator is a successful tool for constructing families of orthogonal polynomials and investigating some approximation problems (cf. [11–14]). For some recent results ... See full document
18
Variational method to a fractional impulsive \((p,q)\) Laplacian coupled systems with partial sub \((p,q)\) linear growth
... important applications of fractional differential equations to engineering, physics, chemistry and biology, the existence and multiplicity of solutions for fractional differential ... See full document
14
A generalized q fractional Gronwall inequality and its applications to nonlinear delay q fractional difference systems
... a new discrete q-fractional version of the Gronwall ...the q-Mittag-Leffler function is ...Caputo q-fractional difference ... See full document
13
Matrix Mittag-Leffler functions of fractional nabla calculus
... nabla calculus is a new branch of mathematics which deals with arbitrary order sums and differences and their properties in nabla ...of fractional nabla difference dates back to the works of ... See full document
13
Local existence for an impulsive fractional neutral integro differential system with Riemann–Liouville fractional derivatives in a Banach space
... an impulsive fractional semilinear integro-differential equation with non- compact ...RL fractional system with the help of the Banach contraction principle in a Banach ...of impulsive ... See full document
26
Existence and Ulam stability for implicit fractional q difference equations
... Fractional q-difference equations were initiated in the beginning of the 19th century [7, 15], and received significant attention in recent ...of q-difference and fractional ... See full document
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