Browsing by Author "Agarwal, Ravi P."

Now showing 1 - 20 of 36

Citation - WoS: 13
Citation - Scopus: 15
A Remark on the Fractional Integral Operators and the Image Formulas of Generalized Lommel-Wright Function
(Frontiers Media Sa, 2018) Agarwal, Ritu; Baleanu, Dumitru; Jain, Sonal; Agarwal, Ravi P.; Baleanu, Dumitru; 56389; Matematik
In this paper, the operators of fractional integration introduced by Marichev-Saigo-Maeda involving Appell's function F-3(center dot) are applied, and several new image formulas of generalized Lommel-Wright function are established. Also, by implementing some integral transforms on the resulting formulas, few more image formulas have been presented. We can conclude that all derived results in our work generalize numerous well-known results and are capable of yielding a number of applications in the theory of special functions. Primary: 44A20 Transforms of special functions; 65R10 For numerical methods; 26A33 Fractional derivatives and integrals; Secondary: 33C20 Generalized hypergeometric series, pFq; 33E50 Special functions in characteristic p (gamma functions, etc.); 2010 AMS classification by MathSciNet
Citation - WoS: 156
Citation - Scopus: 169
A survey on fuzzy fractional differential and optimal control nonlocal evolution equations
(Elsevier, 2018) Agarwal, Ravi P.; Baleanu, Dumitru; Baleanu, Dumitru; Nieto, Juan J.; Torres, Delfim F. M.; Zhou, Yong; 56389; Matematik
We survey some representative results on fuzzy fractional differential equations, controllability, approximate controllability, optimal control, and optimal feedback control for several different kinds of fractional evolution equations. Optimality and relaxation of multiple control problems, described by nonlinear fractional differential equations with nonlocal control conditions in Banach spaces, are considered. (C) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 53
Citation - Scopus: 61
A survey:F-contractions with related fixed point results
(Springer Basel Ag, 2020) Karapinar, Erdal; Karapınar, Erdal; Fulga, Andreea; Agarwal, Ravi P.; 19184; Matematik
In this note, we aim to review the recent results onF-contractions, introduced by Wardowski. After examining the fixed point results for such operators, we collect the sequent results in this direction in a different setting. One of the aims of this survey is to provide a complete collection of several fixed generalizations and extensions ofF-contractions.
Citation - WoS: 102
Citation - Scopus: 104
An existence result for a superlinear fractional differential equation
(Pergamon-elsevier Science Ltd, 2010) Baleanu, Dumitru; Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Matematik
We establish the existence and uniqueness of solution for the boundary value problem D-0(t)alpha(x') + a(t)x(lambda) = 0, t > 0, x' (0) = 0, lim(t ->+infinity) x(t) = 1, where D-0(t)alpha designates the Riemann-Liouville derivative of order alpha epsilon (0, 1) and lambda > 1. Our result might be useful for establishing a non-integer variant of the Atkinson classical theorem on the oscillation of Emden-Fowler equations. (C) 2010 Elsevier Ltd. All rights reserved.
Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations
(2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389; Matematik
We establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0
Asymptotic integration of (1+alpha)-order fractional differential equations
(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Matematik
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0.
Asymptotic Integration of (1+Alpha)-Order Fractional Differential Equations
(Pergamon-Elsevier Science LTD, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389; Matematik
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 28
Citation - Scopus: 30
Asymptotic integration of (1+alpha)-order fractional differential equations
(Pergamon-elsevier Science Ltd, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; 56389; Matematik
We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 24
Citation - Scopus: 32
Asymptotic integration of some nonlinear differential equations with fractional time derivative
(Iop Publishing Ltd, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Ravi P.; Mustafa, Octavian G.; Cosulschi, Mirel; Matematik
We establish that, under some simple integral conditions regarding the nonlinearity, the (1 + alpha)-order fractional differential equation D-0(t)alpha (x') + f (t, x) = 0, t > 0, has a solution x is an element of C([0, +infinity), R) boolean AND C-1((0, +infinity), R), with lim(t SE arrow 0) [t(1-alpha)x'(t)] is an element of R, which can be expanded asymptotically as a+bt(alpha)+O(t(alpha-1)) when t ->+infinity for given real numbers a, b. Our arguments are based on fixed point theory. Here, D-0(t)alpha designates the Riemann-Liouville derivative of order alpha is an element of (0, 1).
Citation - WoS: 15
Citation - Scopus: 28
Asymptotically linear solutions for some linear fractional differential equations
(Hindawi Publishing Corporation, 2010) Baleanu, Dumitru; Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Matematik
We establish here that under some simple restrictions on the functional coefficient a(t) the fractional differential equation 0D(t)(alpha)[tx' - x + x(0)] + a(t)x = 0, t > 0, has a solution expressible as ct + d + o(1) for t -> +infinity, where D-0(t)alpha designates the Riemann-Liouville derivative of order alpha is an element of (0, 1) and c, d is an element of R.
Citation - WoS: 17
Citation - Scopus: 19
Existence and uniqueness of positive solutions to fractional boundary value problems with nonlinear boundary conditions
(Springer, 2013) Nyamoradi, Nemat; Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Ravi P.; 56389; Matematik
In this manuscript, we consider two problems of boundary value problems for a fractional differential equation. A fixed point theorem in partially ordered sets and a contraction mapping principle are applied to prove the existence of at least one positive solution for both fractional boundary value problems.
Citation - WoS: 9
Citation - Scopus: 10
Extended suprametric spaces and Stone-type theorem
(Amer inst Mathematical Sciences-aims, 2023) Panda, Sumati Kumari; Karapınar, Erdal; Agarwal, Ravi P.; Karapinar, Erdal; 19184; Matematik
Extended suprametric spaces are defined, and the contraction principle is established using elementary properties of the greatest lower bound instead of the usual iteration procedure. Thereafter, some topological results and the Stone-type theorem are derived in terms of suprametric spaces. Also, we have shown that every suprametric space is metrizable. Further, we prove the existence of a solution of Ito-Doob type stochastic integral equations using our main fixed point theorem in extended suprametric spaces.
Citation - WoS: 46
Citation - Scopus: 49
F-contraction mappings on metric-like spaces in connection with integral equations on time scales
(Springer-verlag Italia Srl, 2020) Agarwal, Ravi P.; Karapınar, Erdal; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; 19184; Matematik
In this paper we investigate the existence and uniqueness of fixed points of certain (phi,F)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results.
Fixed Point Theory in Generalized Metric Spaces
(2022) Karapınar, Erdal; Agarwal, Ravi P.; 19184; Matematik
This book presents fixed point theory, one of the crucial tools in applied mathematics, functional analysis, and topology, which has been used to solve distinct real-world problems in computer science, engineering, and physics. The authors begin with an overview of the extension of metric spaces. Readers are introduced to general fixed-point theorems while comparing and contrasting important and insignificant metric spaces. The book is intended to be self-contained and serves as a unique resource for researchers in various disciplines.
Citation - WoS: 6
Citation - Scopus: 8
Fixed-Point Results for Meir–Keeler Type Contractions in Partial Metric Spaces: A Survey
(Mdpi, 2022) Karapinar, Erdal; Karapınar, Erdal; Agarwal, Ravi P.; Yesilkaya, Seher Sultan; Wang, Chao; 19184; Matematik
In this paper, we aim to review Meir-Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler's contraction.
Citation - WoS: 101
Citation - Scopus: 95
Fractional calculus in the sky
(Springer, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Ravi P.; 56389; Matematik
Fractional calculus was born in 1695 on September 30 due to a very deep question raised in a letter of L'Hospital to Leibniz. The prophetical answer of Leibniz to that deep question encapsulated a huge inspiration for all generations of scientists and is continuing to stimulate the minds of contemporary researchers. During 325 years of existence, fractional calculus has kept the attention of top level mathematicians, and during the last period of time it has become a very useful tool for tackling the dynamics of complex systems from various branches of science and engineering. In this short manuscript, we briefly review the tremendous effect that the main ideas of fractional calculus had in science and engineering and briefly present just a point of view for some of the crucial problems of this interdisciplinary field.
Citation - WoS: 2
Citation - Scopus: 2
Fractional evolution equation with Cauchy data in spaces
(Springer, 2022) Nguyen Duc Phuong; Baleanu, Dumitru; Baleanu, Dumitru; Agarwal, Ravi P.; Le Dinh Long; 56389; Matematik
In this paper, we consider the Cauchy problem for fractional evolution equations with the Caputo derivative. This problem is not well posed in the sense of Hadamard. There have been many results on this problem when data is noisy in L-2 and H-s,H- However, there have not been any papers dealing with this problem with observed data in L-p with p not equal 2. We study three cases of source functions: homogeneous case, inhomogeneous case, and nonlinear case. For all of them, we use a truncation method to give an approximate solution to the problem. Under different assumptions on the smoothness of the exact solution, we get error estimates between the regularized solution and the exact solution in L-p. To our knowledge, L-p evaluations for the inverse problem are very limited. This work generalizes some recent results on this problem.
Citation - WoS: 7
Citation - Scopus: 12
Fractional Hybrid Differential Equations and Coupled Fixed-Point Results for Α-Admissible F(Ψ1, Ψ2)-Contractions in M-Metric Spaces
(Hindawi Ltd, 2020) Karapinar, Erdal; Moustafa, Shimaa, I; Shehata, Ayman; Agarwal, Ravi P.
In this paper, we investigate the existence of a unique coupled fixed point for alpha-admissible mapping which is of F(psi(1),psi(2))-contraction in the context ofM-metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.
Citation - WoS: 16
Citation - Scopus: 66
Fractional sums and differences with binomial coefficients
(Hindawi Ltd, 2013) Abdeljawad, Thabet; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Jarad, Fahd; Jarad, Fahd; Agarwal, Ravi P.; Matematik
In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives. The second approach is by iterating the derivative and then defining a fractional order by making use of the binomial theorem to obtain Grunwald-Letnikov fractional derivatives. In this paper we formulate the delta and nabla discrete versions for left and right fractional integrals and derivatives representing the second approach. Then, we use the discrete version of the Q-operator and some discrete fractional dual identities to prove that the presented fractional differences and sums coincide with the discrete Riemann ones describing the first approach.
FractionalHybridDifferential EquationsandCoupled Fixed-Point Results for α-Admissible F(ψ1, ψ2) − Contractions in M − Metric Spaces
(2020) Karapınar, Erdal; Shimaa I., Moustafa; Shehata, Ayman; Agarwal, Ravi P.; 19184; Matematik
In this paper, we investigate the existence of a unique coupled fixed point for admissible mapping which is of contraction in the context of metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.