Browsing by Author "Mohammed, Pshtiwan Othman"

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Citation - WoS: 27
Citation - Scopus: 27
Some New Fractional Estimates of Inequalities for Lr-P Interval-Valued Functions by Means of Pseudo Order Relation
(Mdpi, 2021) Mohammed, Pshtiwan Othman; Noor, Muhammad Aslam; Baleanu, Dumitru; Garcia Guirao, Juan Luis; Khan, Muhammad Bilal
It is a familiar fact that interval analysis provides tools to deal with data uncertainty. In general, interval analysis is typically used to deal with the models whose data are composed of inaccuracies that may occur from certain kinds of measurements. In interval analysis, both the inclusion relation (subset of) and pseudo order relation (<= p) are two different concepts. In this article, by using pseudo order relation, we introduce the new class of nonconvex functions known as LR-p-convex interval-valued functions (LR-p-convex-IVFs). With the help of this relation, we establish a strong relationship between LR-p-convex-IVFs and Hermite-Hadamard type inequalities (HH-type inequalities) via Katugampola fractional integral operator. Moreover, we have shown that our results include a wide class of new and known inequalities for LR-p-convex-IVFs and their variant forms as special cases. Useful examples that demonstrate the applicability of the theory proposed in this study are given. The concepts and techniques of this paper may be a starting point for further research in this area.
Citation - WoS: 22
Citation - Scopus: 21
Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels
(Mdpi, 2022) Srivastava, Hari Mohan; Baleanu, Dumitru; Abualnaja, Khadijah M.; Mohammed, Pshtiwan Othman
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: 18
Citation - Scopus: 19
Relationships Between the Discrete Riemann-Liouville and Liouville-Caputo Fractional Differences and Their Associated Convexity Results
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Abualrub, Marwan S.; Guirao, Juan L. G.
In this study, we have presented two new alternative definitions corresponding to the basic definitions of the discrete delta and nabla fractional difference operators. These definitions and concepts help us in establishing a relationship between Riemann-Liouville and Liouville-Caputo fractional differences of higher orders for both delta and nabla operators. We then propose and analyse some convexity results for the delta and nabla fractional differences of the Riemann-Liouville type. We also derive similar results for the delta and nabla fractional differences of Liouville-Caputo type by using the proposed relationships. Finally, we have presented two examples to confirm the main theorems.
Citation - WoS: 2
Citation - Scopus: 2
Analysing Discrete Fractional Operators With Exponential Kernel for Positivity in Lower Boundedness
(Amer inst Mathematical Sciences-aims, 2022) Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Aydi, Hassen; Hamed, Yasser S.; Mahmood, Sarkhel Akbar
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: 24
Citation - Scopus: 27
New Discrete Inequalities of Hermite-Hadamard Type for Convex Functions
(Springer, 2021) Alqudah, Manar A.; Jarad, Fahd; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet
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: 3
Citation - Scopus: 3
Monotonicity and Extremality Analysis of Difference Operators in Riemann-Liouville Family
(Amer inst Mathematical Sciences-aims, 2023) Abdeljawad, Thabet; Al-Sarairah, Eman; Hamed, Y. S.; Mohammed, Pshtiwan Othman; Baleanu, Dumitru
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: 6
Citation - Scopus: 6
A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting
(Mdpi, 2023) Mohammed, Pshtiwan Othman; Guirao, Juan Luis G.; Baleanu, Dumitru; Al-Sarairah, Eman; Jan, Rashid; Srivastava, Hari Mohan
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: 93
Citation - Scopus: 112
On the Generalized Hermite-Hadamard Inequalities Via the Tempered Fractional Integrals
(Mdpi, 2020) Sarikaya, Mehmet Zeki; Baleanu, Dumitru; Mohammed, Pshtiwan Othman
Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of lambda-incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite-Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann-Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.
Citation - WoS: 24
Citation - Scopus: 25
Some Modifications in Conformable Fractional Integral Inequalities
(Springer, 2020) Mohammed, Pshtiwan Othman; Vivas-Cortez, Miguel; Rangel-Oliveros, Yenny; Baleanu, Dumitru
The prevalence of the use of integral inequalities has dramatically influenced the evolution of mathematical analysis. The use of these useful tools leads to faster advances in the presentation of fractional calculus. This article investigates the Hermite-Hadamard integral inequalities via the notion of F-convexity. After that, we introduce the notion of F-mu-convexity in the context of conformable operators. In view of this, we establish some Hermite-Hadamard integral inequalities (both trapezoidal and midpoint types) and some special case of those inequalities as well. Finally, we present some examples on special means of real numbers. Furthermore, we offer three plot illustrations to clarify the results.
Citation - WoS: 14
Citation - Scopus: 14
Novel Algorithms To Approximate the Solution of Nonlinear Integro-Differential Equations of Volterra-Fredholm Integro Type
(Amer inst Mathematical Sciences-aims, 2023) Srivastava, Hari Mohan; Hama, Mudhafar; Mohammed, Pshtiwan Othman; Almusawa, Musawa Yahya; Baleanu, Dumitru; HamaRashid, Hawsar
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: 8
Analytical and Numerical Negative Boundedness of Fractional Differences With Mittag-Leffler Kernel
(Amer inst Mathematical Sciences-aims, 2023) Dahal, Rajendra; Hamed, Y. S.; Goodrich, Christopher S.; Baleanu, Dumitru; Mohammed, Pshtiwan Othman
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: 27
Citation - Scopus: 29
Existence and Uniqueness of Uncertain Fractional Backward Difference Equations of Riemann-Liouville Type
(Hindawi Ltd, 2020) Jarad, Fahd; Chu, Yu-Ming; Mohammed, Pshtiwan Othman; Abdeljawad, Thabet
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: 10
Citation - Scopus: 12
Fuzzy-Interval Inequalities for Generalized Convex Fuzzy-Interval Functions Via Fuzzy Riemann Integrals
(Amer inst Mathematical Sciences-aims, 2022) Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Jawa, Taghreed M.; Khan, Muhammad Bilal
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: 3
Citation - Scopus: 4
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: 21
Citation - Scopus: 28
General Raina Fractional Integral Inequalities on Coordinates of Convex Functions
(Springer, 2021) Kashuri, Artion; Mohammed, Pshtiwan Othman; Meftah, Badreddine; Baleanu, Dumitru
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: 4
Citation - Scopus: 4
Positivity Analysis for Mixed Order Sequential Fractional Difference Operators
(Amer inst Mathematical Sciences-aims, 2022) Abdeljawad, Thabet; Sahoo, Soubhagya Kumar; Abualnaja, Khadijah M.; Mohammed, Pshtiwan Othman; Baleanu, Dumitru
We consider the positivity of the discrete sequential fractional operators ((RL)(a0+1) del(v1) (RL)(a0) del(v2) f) (tau) defined on the set D-1 (see (1.1) and Figure 1) and (RL)(a0+2) del(v1) (RL)(a0) del(v2) f) (tau) of mixed order defined on the set D-2 (see (1.2) and Figure 2) for tau is an element of N-a0. By analysing the first sequential operator, we reach that (del f(tau) >= 0; for each tau is an element of Na0+1. Besides, we obtain (del f(tau) >= 0 by analysing the second sequential operator. Furthermore, some conditions to obtain the proposed monotonicity results are summarized. Finally, two practical applications are provided to illustrate the efficiency of the main theorems.
Citation - WoS: 8
Citation - Scopus: 8
Positivity Analysis for the Discrete Delta Fractional Differences of the Riemann-Liouville and Liouville-Caputo Types
(Amer inst Mathematical Sciences-aims, 2022) Srivastava, Hari Mohan; Baleanu, Dumitru; Elattar, Ehab E.; Hamed, Y. S.; Mohammed, Pshtiwan Othman
In this article, we investigate some new positivity and negativity results for some families of discrete delta fractional difference operators. A basic result is an identity which will prove to be a useful tool for establishing the main results. Our first main result considers the positivity and negativity of the discrete delta fractional difference operator of the Riemann-Liouville type under two main conditions. Similar results are then obtained for the discrete delta fractional difference operator of the Liouville-Caputo type. Finally, we provide a specific example in which the chosen function becomes nonincreasing on a time set.
Citation - WoS: 8
Citation - Scopus: 8
On Convexity Analysis for Discrete Delta Riemann-Liouville Fractional Differences Analytically and Numerically
(Springer, 2023) Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y. S.; Baleanu, Dumitru; Mohammed, Pshtiwan Othman
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.
Citation - WoS: 47
Citation - Scopus: 49
Hermite-Hadamard Type Inequalities for Interval-Valued Preinvex Functions Via Fractional Integral Operators
(Springernature, 2022) Sahoo, Soubhagya Kumar; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Kodamasingh, Bibhakar; Srivastava, Hari Mohan
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: 4
Citation - Scopus: 3
Theoretical and Numerical Computations of Convexity Analysis for Fractional Differences Using Lower Boundedness
(World Scientific Publ Co Pte Ltd, 2023) Al-Sarairah, Eman; Abdeljawad, Thabet; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman; Baleanu, Dumitru
This study focuses on the analytical and numerical solutions of the convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and nonnegative lower bounds. In the analytical part of the paper, we will give a new formula for del(2) of the discrete fractional differences, which can be useful to obtain the convexity results. The correlation between the nonnegativity and negativity of both of the discrete fractional differences, ((CFR)(a)del(alpha)f)(t) and ((ABR)(a)del(alpha)f)(t), with the convexity of the functions will be examined. In light of the main lemmas, we will define the two decreasing subsets of (2, 3), namely H-k,H-epsilon and M-k,M-epsilon. The decrease of these sets enables us to obtain the relationship between the negative lower bound of ((CFR)(a)del(alpha)f)(t) and the convexity of the function on a finite time set given by N-a+1(P) := {a + 1, a + 2,..., P}, for some P is an element of Na+1 := {a + 1, a + 2,...}. Besides, the numerical part of the paper is dedicated to examine the validity of the sets H-k,H- is an element of and M-k,M- is an element of in certain regions of the solutions for different values of k and is an element of. For this reason, we will illustrate the domain of the solutions by means of several figures in which the validity of the main theorems are explained.