Browsing by Author "Srivastava, Hari Mohan"

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Citation Count: Srivastava, Hari Mohan...et.al. (2023). "A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting", Symmetry-Basel, Vol.15, No.2.
A Study of Positivity Analysis for Difference Operators in the Liouville-Caputo Setting
(2023) Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Guirao, Juan Luis G.; Baleanu, Dumitru; Al-Sarairah, Eman; Jan, Rashid; : 56389
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 Count: Srivastava, Hari Mohan...et al. (2021). "Fractional integral inequalities for exponentially nonconvex functions and their applications", Fractal and Fractional, Vol. 5, No. 3.
Fractional integral inequalities for exponentially nonconvex functions and their applications
(2021) Srivastava, Hari Mohan; Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y.S.; 56389
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. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
Citation Count: Khan, Muhammad Bilal...et al. (2022). "Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals", AIMS Mathematics, Vol. 7, No. 1, pp. 1507-1535.
Fuzzy-interval inequalities for generalized convex fuzzy-interval-valued functions via fuzzy Riemann integrals
(2022) Khan, Muhammad Bilal; Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Jawa, Taghreed M.; 56389
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-Fejér type inequality (H-H Fejér 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.©2022 the Author(s), licensee AIMS Press. © 2022, American Institute of Mathematical Sciences. All rights reserved.
Citation Count: Srivastava, Hari Mohan;...et.al. (2022). "Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators", International Journal of Computational Intelligence Systems, Vol.15, No.1.
Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators
(2022) Srivastava, Hari Mohan; Sahoo, Soubhagya Kumar; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Kodamasingh, Bibhakar; 56389
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 Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Introduction to local fractional derivative and integral operators", Local Fractional Integral Transforms and Their Applications, pp. 1-55, (2016).
Introduction to local fractional derivative and integral operators
(Elsevier Science LTD, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, Hari Mohan; 56389
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Local fractional Fourier transform and applications", Local Fractional Integral Transforms and Their Applications, pp. 95-145, (2016).
Local fractional Fourier transform and applications
(Elsevier Science LTD, 2016) Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, Hari Mohan; 56389
Citation Count: Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M., "Local fractional Laplace transform and applications", Local Fractional Integral Transforms and Their Applications, pp. 147-178, (2016).
Local fractional Laplace transform and applications
(Elsevier Science LTD, 2016) Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, Hari Mohan; 56389
Citation Count: Mohammed, Pshtiwan Othman;...et.al. (2022). "Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels", Symmetry, Vol.14, No.8.
Modified Fractional Difference Operators Defined Using Mittag-Leffler Kernels
(2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Abualnaja, Khadijah M.; 56389
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 Count: Mohammed, Pshtiwan Othman;...et.al. (2023). "Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels", Journal of King Saud University - Science, Vol35, No.7.
Monotonicity and positivity analyses for two discrete fractional-order operator types with exponential and Mittag–Leffler kernels
(2023) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Al-Sarairah, Eman; Sahoo, Soubhagya Kumar; Chorfi, Nejmeddine; 56389
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<φ<2, as well as between 1<φ<[Formula presented]. 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 ∇Q(τ) 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 ∇Q(τ) in the Liouville-Caputo sense by utilizing this relationship. Two examples are presented to validate the results.
Citation Count: Hamarashid, Hawsar;...et.al. (2023). "Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type", AIMS Mathematics, Vol.8, no.6, pp.14572-14591.
Novel algorithms to approximate the solution of nonlinear integro-differential equations of Volterra-Fredholm integro type
(2023) Hamarashid, Hawsar; Srivastava, Hari Mohan; Hama, Mudhafar; Mohammed, Pshtiwan Othman; Almusawa, Musawa Yahya; Baleanu, Dumitru; 56389
This study is devoted to examine the existence and uniqueness behavior of a nonlinear integro-di_erential 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 conditions are developed to prove the proposed model’s continues behavior which reflects the stable generation. At last, three test examples are presented to verify the established theoretical concepts.
Citation Count: Baleanu, D.;...et.al. (2023). "On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically", Journal of Inequalities and Applications, Vol.2023, no.1.
On convexity analysis for discrete delta Riemann–Liouville fractional differences analytically and numerically
(2023) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Al-Sarairah, Eman; Abdeljawad, Thabet; Hamed, Y.S.; 56389
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 Δ 2, which will be useful to obtain the convexity results. We examine the correlation between the positivity of (w0RLΔαf)(t) and convexity of the function. In view of the basic lemmas, we define two decreasing subsets of (2 , 3 ) , Hk,ϵ and Mk,ϵ. The decrease of these sets allows us to obtain the relationship between the negative lower bound of (w0RLΔαf)(t) and convexity of the function on a finite time set Nw0P:={w0,w0+1,w0+2,…,P} for some P∈Nw0:={w0,w0+1,w0+2,…}. The numerical part of the paper is dedicated to examinin the validity of the sets Hk,ϵ and Mk,ϵ for different values of k and ϵ. For this reason, we illustrate the domain of solutions via several figures explaining the validity of the main theorem.
Citation Count: Mohammed, Pshtiwan Othman;...et.al. (2022). "Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types", Electronic Research Archive, Vol.30, No.8, pp.3058-3070.
Positivity analysis for the discrete delta fractional differences of the Riemann-Liouville and Liouville-Caputo types
(2022) Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Elattar, Ehab E.; Hamed, Y. S.; 56389
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 Count: Baleanu, Dumitru; Srivastava, Hari Mohan; Cattani, Carlo (2022). "Recent advances in computational biology", Chaos Solitons & Fractals, Vol. 163.
Recent advances in computational biology
(2022) Baleanu, Dumitru; Srivastava, Hari Mohan; Cattani, Carlo; 56389
Citation Count: Guirao, Juan L. G.;...et.al. (2022). "Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results", AIMS Mathematics, Vol.7, No.10, pp.18127-18141.
Relationships between the discrete Riemann-Liouville and Liouville-Caputo fractional differences and their associated convexity results
(2022) Guirao, Juan L. G.; Mohammed, Pshtiwan Othman; Srivastava, Hari Mohan; Baleanu, Dumitru; Abualrub, Marwan S.; 56389
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.