Explicit solutions of a certain class of differential equations by means of fractional calculus

Srivástava, H. M.; Lin, Shy‐Der; Chao, Yi-Ting; Wang, Pin-Yu

doi:10.1134/s1061920807030090

Cited by 4 publications

(3 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition to this, projection neural networks have emerged out as a promising tool in the field of fractional calculus also. Due to wide application in almost all branches of sciences, fractional differential equations have received remarkable attention in the field of mechanics, physics, chemistry, informatics, materials and several other applications [22,23]. To the best of our knowledge, very few results are available in literature for projection neural networks in the field of fractional calculus [24,25].…”

Section: Introductionmentioning

confidence: 99%

Stability and synchronization of delayed fractional-order projection neural network with piecewise constant argument of mixed type

Tyagi

Abbas

2017

Tbilisi Math. J.

View full text Add to dashboard Cite

Projection equations arise in several optimization problems and possess significant applications in many areas of science and engineering. In this paper, we propose a fractional-order projection neural network to solve quadratic programming problems. We study stability and synchronization for a class of delayed projection neural networks of mixed type via impulsive control. Using concepts of fractional calculus, we investigate the existence of solution and study its global asymptotic stability. Moreover, we propose an effective impulsive control scheme to achieve synchronization for the system. We demonstrate the validity and transient behaviour of the proposed neural network with the help of suitable examples.

show abstract

Section: Introductionmentioning

confidence: 99%

Stability and synchronization of delayed fractional-order projection neural network with piecewise constant argument of mixed type

Tyagi

Abbas

2017

Tbilisi Math. J.

View full text Add to dashboard Cite

show abstract

“…On the other hand, the study for solutions of fractional ordinary and partial differential equations has received great interest by scientists. Especially, in the last decade, there are noteworthy works on the analytical and numerical solutions of fractional partial differential equations see [21][22][23][24][25][26][27][28] and the references there in .…”

Section: Introductionmentioning

confidence: 99%

Existence Results for Solutions of Nonlinear Fractional Differential Equations

Yakar

Köksal

2012

Abstract and Applied Analysis

View full text Add to dashboard Cite

This paper deals with theoretical and constructive existence results for solutions of nonlinear fractional differential equations using the method of upper and lower solutions which generate a closed set. The existence of solutions for nonlinear fractional differential equations involving Riemann-Liouville differential operator in a closed set is obtained by utilizing various types of coupled upper and lower solutions. Furthermore, these results are extended to the finite systems of nonlinear fractional differential equations leading to more general results.

show abstract

“…The main purpose of this section (and Section 7 below) is to follow rather closely and analogously the investigations in (for example) [16], [23], [53], [63] and [64] of solutions of some general families of second-order linear ordinary differential equations, which are associated with the familiar Bessel differential equation of general order ν (cf. [5], Vol.…”

Section: The Classical Gauss and Jacobi Differential Equations Revisitedmentioning

confidence: 99%

An Elementary and Introductory Approach to Fractional Calculus and Its Applications

Srivástava¹

2017

Contributions

View full text Add to dashboard Cite

A b s t r a c t: The subject of fractional calculus (that is, calculus of integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, due mainly to its demonstrated applications in numerous seemingly diverse and widespread fields of science and engineering. It does indeed provide several potentially useful tools for solving differential and integral equations, and various other problems involving special functions of mathematical physics as well as their extensions and generalizations in one and more variables. The main object of this paper * is to present a brief elementary and introductory approach to the theory of fractional calculus and its applications especially in developing solutions of certain interesting families of ordinary and partial fractional differintegral equations. Relevant connections of some of the results presented in this lecture with those obtained in many other earlier works on this subject will also be indicated.

show abstract

Explicit solutions of a certain class of differential equations by means of fractional calculus

Cited by 4 publications

References 11 publications

Stability and synchronization of delayed fractional-order projection neural network with piecewise constant argument of mixed type

Stability and synchronization of delayed fractional-order projection neural network with piecewise constant argument of mixed type

Existence Results for Solutions of Nonlinear Fractional Differential Equations

An Elementary and Introductory Approach to Fractional Calculus and Its Applications

Contact Info

Product

Resources

About