FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

doi:10.1016/S0252-9602(16)30052-2

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (3): 957-970.doi: 10.1016/S0252-9602(16)30052-2

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FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

Dhananjay GOPAL¹, Mujahid ABBAS², Deepesh Kumar PATEL³, Calogero VETRO⁴

1. Department of Applied Mathematics & Humanities, S. V. National Institute of Technology, Surat-395007, Gujarat, India;
2. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria 0002, South Africa;Department of Mathematics, King AbdulAziz University, P. O. Box 80203 Jeddah 21589, Saudi Arabia;
3. Department of Mathematics Visvesvaraya National Institute of Technology, Nagpur-440010, Maharashtra, India;
4. Università degli Studi di Palermo, Dipartimento di Matematica e Informatica, Via Archirafi, 34-90123 Palermo, Italy

Received:2015-08-26 Revised:2015-12-06 Online:2016-06-25 Published:2016-06-25
Contact: Dhananjay GOPAL,E-mail:dg@ashd.svnit.ac.in,gopaldhananjay@yahoo.in E-mail:dg@ashd.svnit.ac.in,gopaldhananjay@yahoo.in

Abstract

Abstract:

In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in[21, 22] and differ-ent from α-GF-contractions given in[8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an appli-cation to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

Key words: fixed points, nonlinear fractional differential equations, periodic points

CLC Number:

37C25

Dhananjay GOPAL, Mujahid ABBAS, Deepesh Kumar PATEL, Calogero VETRO. FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION[J].Acta mathematica scientia,Series B, 2016, 36(3): 957-970.

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References

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FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

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