Browsing by Author "Mohammed, Pshtiwan Othman"

Now showing 1 - 20 of 27

Citation - WoS: 6
Citation - Scopus: 6
A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting
(Mdpi, 2023) Srivastava, Hari Mohan; Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Guirao, Juan Luis G.; Baleanu, Dumitru; Al-Sarairah, Eman; Jan, Rashid; : 56389; Matematik
The class of symmetric function interacts extensively with other types of functions. One of these is the class of positivity of functions, which is closely related to the theory of symmetry. Here, we propose a positive analysis technique to analyse a class of Liouville-Caputo difference equations of fractional-order with extremal conditions. Our monotonicity results use difference conditions ((LC)(a)delta(mu)f) (a + J(0) + 1 - mu) >= (1 - mu)f(a + J(0))and ((LC)(a)delta(mu)f) (a + J(0) + 1 -mu) <= (1 - mu)f (a + J(0)) to derive the corresponding relative minimum and maximum, respectively. We find alternative conditions corresponding to the main conditions in the main monotonicity results, which are simpler and stronger than the existing ones. Two numerical examples are solved by achieving the main conditions to verify the obtained monotonicity results.
Citation - WoS: 2
Citation - Scopus: 2
Analysing discrete fractional operators with exponential kernel for positivity in lower boundedness
(Amer inst Mathematical Sciences-aims, 2022) Mahmood, Sarkhel Akbar; Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Aydi, Hassen; Hamed, Yasser S.; 56389; Matematik
In this paper we study the positivity analysis problems for discrete fractional operators with exponential kernel, namely the discrete Caputo-Fabrizio operators. The results are applied to a discrete Caputo-Fabrizio-Caputo fractional operator of order omega of another discrete Caputo-Fabrizio-Riemann fractional operator of order beta. Furthermore, the results are obtained for these operators with having the same orders. The conditions for the discrete fractional operators with respect to negative lower bound conditions are expressed in terms of a positive epsilon.
Citation - WoS: 4
Citation - Scopus: 4
Analysis of positivity results for discrete fractional operators by means of exponential kernels
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; O'Regan, Donal; Brzo, Aram Bahroz; Abualnaja, Khadijah M.; Baleanu, Dumitru; 56389; Matematik
In this study, we consider positivity and other related concepts such as alpha-convexity and alpha-monotonicity for discrete fractional operators with exponential kernel. Namely, we consider discrete Delta fractional operators in the Caputo sense and we apply efficient initial conditions to obtain our conclusions. Note positivity results are an important factor for obtaining the composite of double discrete fractional operators having different orders.
Citation - WoS: 7
Citation - Scopus: 8
Analytical and numerical negative boundedness of fractional differences with Mittag-Leffler kernel
(Amer inst Mathematical Sciences-aims, 2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Dahal, Rajendra; Goodrich, Christopher S.; Hamed, Y. S.; Baleanu, Dumitru; 56389; Matematik
We show that a class of fractional differences with Mittag-Leffler kernel can be negative and yet monotonicity information can still be deduced. Our results are complemented by numerical approximations. This adds to a growing body of literature illustrating that the sign of a fractional difference has a very complicated and subtle relationship to the underlying behavior of the function on which the fractional difference acts, regardless of the particular kernel used.
Citation - WoS: 0
Citation - Scopus: 0
Analytical results for positivity of discrete fractional operators with approximation of the domain of solutions
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; O'Regan, Donal; Baleanu, Dumitru; Hamed, Y. S.; Elattar, Ehab E.; 56389; Matematik
We study the monotonicity method to analyse nabla positivity for discrete fractional operators of Riemann-Liouville type based on exponential kernels, where ((CFR)(c0)del F-theta)(t) > -epsilon Lambda(theta - 1) (del F)(c(0) + 1) such that (del F)(c(0) + 1) >= 0 and epsilon > 0. Next, the positivity of the fully discrete fractional operator is analyzed, and the region of the solution is presented. Further, we consider numerical simulations to validate our theory. Finally, the region of the solution and the cardinality of the region are discussed via standard plots and heat map plots. The figures confirm the region of solutions for specific values of epsilon and theta.
Citation - WoS: 24
Citation - Scopus: 26
Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann-Liouville Type
(Hindawi Ltd, 2020) Abdeljawad, Thabet; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; Jarad, Fahd; Jarad, Fahd; Chu, Yu-Ming; 234808; Matematik
In this article, we consider the analytic solutions of the uncertain fractional backward difference equations in the sense of Riemann-Liouville fractional operators which are solved by using the Picard successive iteration method. Also, we consider the existence and uniqueness theorem of the solution to an uncertain fractional backward difference equation via the Banach contraction fixed-point theorem under the conditions of Lipschitz constant and linear combination growth. Finally, we point out some examples to confirm the validity of the existence and uniqueness of the solution.
Citation - WoS: 7
Citation - Scopus: 7
Fractional integral inequalities for exponentially nonconvex functions and their applications
(Mdpi, 2021) Srivastava, Hari Mohan; Baleanu, Dumitru; Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y. S.; 56389; Matematik
In this paper, the authors define a new generic class of functions involving a certain modified Fox-Wright function. A useful identity using fractional integrals and this modified Fox-Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite-Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.
Citation - WoS: 10
Citation - Scopus: 12
Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals
(Amer inst Mathematical Sciences-aims, 2022) Khan, Muhammad Bilal; Baleanu, Dumitru; Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Jawa, Taghreed M.; 56389; Matematik
The objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as p-convex fuzzy-interval-valued functions (p-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of p-convex FIVFs, we have presented some Hermite-Hadamard type inequalities (H-H type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejer type inequality (H-H Fejer type inequality) for p-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for p-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.
Citation - WoS: 20
Citation - Scopus: 25
General Raina fractional integral inequalities on coordinates of convex functions
(Springer, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Kashuri, Artion; Mohammed, Pshtiwan Othman; Meftah, Badreddine; 56389; Matematik
Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an (l1,h1)-(l2,h2)-convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the (l1,h1)-(l2,h2)-convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.
Citation - WoS: 41
Citation - Scopus: 43
Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators
(Springernature, 2022) Srivastava, Hari Mohan; Baleanu, Dumitru; Sahoo, Soubhagya Kumar; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Kodamasingh, Bibhakar; 56389; Matematik
In this article, the notion of interval-valued preinvex functions involving the Riemann-Liouville fractional integral is described. By applying this, some new refinements of the Hermite-Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.
Citation - WoS: 32
Inequalities of trapezoidal type involving generalized fractional integrals
(Elsevier, 2020) Baleanu, Dumitru; Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Zeng, Shengda; 56389; Matematik
During the last years several fractional integrals were investigated. Having this idea in mind, in the present article, some new generalized fractional integral inequalities of the trapezoidal type for lambda(phi)-preinvexfunctions, which are differentiable and twice differentiable, are established. Then, by employing those results, we explore the new estimates on trapezoidal type inequalities for classical integral and Riemann-Liouville fractional integrals, respectively. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.
Citation - WoS: 20
Citation - Scopus: 20
Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels
(Mdpi, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Srivastava, Hari Mohan; Baleanu, Dumitru; Abualnaja, Khadijah M.; 56389; Matematik
The discrete fractional operators of Riemann-Liouville and Liouville-Caputo are omnipresent due to the singularity of the kernels. Therefore, convexity analysis of discrete fractional differences of these types plays a vital role in maintaining the safe operation of kernels and symmetry of discrete delta and nabla distribution. In their discrete version, the generalized or modified forms of various operators of fractional calculus are becoming increasingly important from the viewpoints of both pure and applied mathematical sciences. In this paper, we present the discrete version of the recently modified fractional calculus operator with the Mittag-Leffler-type kernel. Here, in this article, the expressions of both the discrete nabla derivative and its counterpart nabla integral are obtained. Some applications and illustrative examples are given to support the theoretical results.
Citation - WoS: 1
Citation - Scopus: 1
Monotonicity and extremality analysis of difference operators in Riemann-Liouville family
(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y. S.; 56389; Matematik
In this paper, we will discuss the monotone decreasing and increasing of a discrete nonpositive and nonnegative function defined on Nr0+1, respectively, which come from analysing the discrete Riemann-Liouville differences together with two necessary conditions (see Lemmas 2.1 and 2.3). Then, the relative minimum and relative maximum will be obtained in view of these results combined with another condition (see Theorems 2.1 and 2.2). We will modify and reform the main two lemmas by replacing the main condition with a new simpler and stronger condition. For these new sufficient for the function to be monotone decreasing or increasing.
Citation - WoS: 4
Citation - Scopus: 4
Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels
(Elsevier, 2023) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; 56389; Matematik
The discrete analysed fractional operator technique was employed to demonstrate positive findings concerning the Atangana-Baleanu and discrete Caputo-Fabrizo fractional operators. Our tests utilized discrete fractional operators with orders between 1 < phi < 2, as well as between 1 < phi < 3/2. We employed the initial values of Mittag-Leffler functions and applied the principle of mathematical induction to ensure the positivity of the discrete fractional operators at each time step. As a result, we observed a significant impact of the positivity of these operators on (del(Q)) (tau) within Np0+1 according to the Riemann- Liouville interpretation. Furthermore, we established a correlation between the discrete fractional operators based on the Liouville-Caputo and Riemann-Liouville definitions. In addition, we emphasized the positivity of (del(Q)) (tau) in the Liouville-Caputo sense by utilizing this relationship. Two examples are presented to validate the results.(c) 2023 The Author(s). Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Citation - WoS: 3
Citation - Scopus: 3
Monotonicity Results for Nabla Riemann-Liouville Fractional Differences
(Mdpi, 2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Balea, Itru; Jan, Rashid; Abualnaja, Khadijah M.
Positivity analysis is used with some basic conditions to analyse monotonicity across all discrete fractional disciplines. This article addresses the monotonicity of the discrete nabla fractional differences of the Riemann-Liouville type by considering the positivity of ((RL)(b0)del(theta)g)(z) combined with a condition on g(b(0)+2), g(b(0)+3) and g(b(0)+4), successively. The article ends with a relationship between the discrete nabla fractional and integer differences of the Riemann-Liouville type, which serves to show the monotonicity of the discrete fractional difference ((RL)(b0)del(theta)g)(z).
Citation - WoS: 8
Citation - Scopus: 8
New classifications of monotonicity investigation for discrete operators with Mittag-Leffler kernel
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Goodrich, Christopher S.; Brzo, Aram Bahroz; Baleanu, Dumitru; Hamed, Yasser S.; 56389; Matematik
This paper deals with studying monotonicity analysis for discrete fractional operators with Mittag-Leffler in kernel. The v-monotonicity definitions, namely v-(strictly) increasing and v-(strictly) decreasing, are presented as well. By examining the basic properties of the proposed discrete fractional operators together with v-monotonicity definitions, we find that the investigated discrete fractional operators will be v(2)-(strictly) increasing or v(2)-(strictly) decreasing in certain domains of the time scale Na:= {a, a + 1, ... }. Finally, the correctness of developed theories is verified by deriving mean value theorem in discrete fractional calculus.
Citation - WoS: 23
Citation - Scopus: 24
New discrete inequalities of Hermite–Hadamard type for convex functions
(Springer, 2021) Abdeljawad, Thabet; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; Jarad, Fahd; Alqudah, Manar A.; Jarad, Fahd; 234808; Matematik
We introduce new time scales on Z. Based on this, we investigate the discrete inequality of Hermite-Hadamard type for discrete convex functions. Finally, we improve our result to investigate the discrete fractional inequality of Hermite-Hadamard type for the discrete convex functions involving the left nabla and right delta fractional sums.
Citation - WoS: 19
Citation - Scopus: 27
New fractional inequalities of Hermite–Hadamard type involving the incomplete gamma functions
(Springer, 2020) Abdeljawad, Thabet; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Kashuri, Artion; Hamasalh, Faraidun; Agarwal, Praveen; 56389; Matematik
A specific type of convex functions is discussed. By examining this, we investigate new Hermite-Hadamard type integral inequalities for the Riemann-Liouville fractional operators involving the generalized incomplete gamma functions. Finally, we expose some examples of special functions to support the usefulness and effectiveness of our results.
Citation - WoS: 13
Citation - Scopus: 13
Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type
(Amer inst Mathematical Sciences-aims, 2023) HamaRashid, Hawsar; Baleanu, Dumitru; Srivastava, Hari Mohan; Hama, Mudhafar; Mohammed, Pshtiwan Othman; Almusawa, Musawa Yahya; Baleanu, Dumitru; 56389; Matematik
This study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-differential equation of Volterra-Fredholm integral type in continues space. Then, we examine its solution by modification of Adomian and homotopy analysis methods numerically. Initially, the proposed model is reformulated into an abstract space, and the existence and uniqueness of solution is constructed by employing Arzela-Ascoli and Krasnoselskii fixed point theorems. Furthermore, suitable generation. At last, three test examples are presented to verify the established theoretical concepts.
Citation - WoS: 7
Citation - Scopus: 7
On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically
(Springer, 2023) Baleanu, Dumitru; Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet; Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y. S.; 56389; Matematik
In this paper, we focus on the analytical and numerical convexity analysis of discrete delta Riemann-Liouville fractional differences. In the analytical part of this paper, we give a new formula for the discrete delta Riemann-Liouville fractional difference as an alternative definition. We establish a formula for the delta(2), which will be useful to obtain the convexity results. We examine the correlation between the positivity of ((RL)(w0)delta(alpha)f)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2, 3), H(k,E )and M-k,M-E. The decrease of these sets allows us to obtain the relationship between the negative lower bound of ((RL)(w0)delta(alpha)f)(t) and convexity of the function on a finite time set N-w0(P) := {w(0), w(0) + 1, w(0) + 2, ,P}for some P is an element of N-w0 := {w(0), w(0) + 1, w(0 )+ 2,...}. The numerical part of the paper is dedicated to examinin the validity of the setsH(k,E)and M-k,M-E for different values of k and E. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.