Browsing by Author "Srivastava, Hari Mohan"

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Citation - Scopus: 1
Editorial: Recent Advances in Computational Biology
(Pergamon-elsevier Science Ltd, 2022) Srivastava, Hari Mohan; Cattani, Carlo; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 7
Citation - Scopus: 7
Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications
(Mdpi, 2021) Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y. S.; Srivastava, Hari Mohan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 46
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 21
Citation - Scopus: 20
Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels
(Mdpi, 2022) Srivastava, Hari Mohan; Baleanu, Dumitru; Abualnaja, Khadijah M.; Mohammed, Pshtiwan Othman; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 4
Citation - Scopus: 4
Monotonicity and Positivity Analyses for Two Discrete Fractional-Order Operator Types With Exponential and Mittag-Leffler Kernels
(Elsevier, 2023) Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 16
Citation - Scopus: 16
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.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 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; : 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.