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On discrete tempered fractional calculus and its application
Discrete tempered fractional calculus, as a fresh generalization of discrete fractional calculus, takes both the advantages of discrete fractional...
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On Taylor’s formulas in fractional calculus: overview and characterization for the Caputo derivative
This paper discusses some aspects of Taylor’s formulas in fractional calculus, focusing on use of Caputo’s definition. Such formulas consist of a...
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Mathematical Foundation of Fractional Calculus
In the long history of the development of fractional calculus, a variety of definitions have been proposed by researchers from different...
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Towards a Unified theory of Fractional and Nonlocal Vector Calculus
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are...
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An eigenvalue problem in fractional h-discrete calculus
In this paper, we prove existence of solutions for an eigenvalue problem in the fractional h -discrete calculus. Dirichlet type boundary conditions...
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Fractional calculus in the sky
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...
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Fractional Bessel Derivative Within the Mellin Transform Framework
In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the...
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Operational Calculus for the General Fractional Derivative and Its Applications
In this paper, we first address the general fractional integrals and derivatives with the Sonine kernels that possess the integrable singularities of...
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Mkhitar Djrbashian and His Contribution to Fractional Calculus
This survey paper is devoted to the description of the results by M.M. Djrbashian related to the modern theory of Fractional Calculus. M.M....
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On the variable-order fractional derivatives with respect to another function
In this paper, we present various concepts concerning generalized fractional calculus, wherein the fractional order of operators is not constant, and...
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Novel results of Milne-type inequalities involving tempered fractional integrals
In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of...
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New error bounds for Newton’s formula associated with tempered fractional integrals
In this paper, we first construct an integral identity associated with tempered fractional operators. By using this identity, we have found the error...
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Fixed-Point Theorems Based Evaluation of Analytical Solution in Fractional Diffusion Equations
The definition of fractional calculus is a careful study conducted by experts in a variety of technical and scientific fields. Fractional calculus is...
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Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications
Mikusiński’s operational calculus is a formalism for understanding integral and derivative operators and solving differential equations, which has...
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Reachability of time-varying fractional dynamical systems with Riemann-Liouville fractional derivative
This study examines the reachability of a time-varying fractional dynamical system with Riemann-Liouville fractional derivative. The state transition...
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Approximate Controllability for Hilfer Fractional Stochastic Non-instantaneous Impulsive Differential System with Rosenblatt Process and Poisson Jumps
This paper discusses the approximate controllability of Hilfer fractional stochastic differential system involving non-instantaneous impulses with...
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Qualitative Analysis of Fractional Stochastic Differential Equations with Variable Order Fractional Derivative
This research paper has been dedicated to the investigation of Coupled System of Fractional Stochastic Differential Equations (CSFSDEs), which is an...
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A novel delayed discrete fractional Mittag-Leffler function: representation and stability of delayed fractional difference system
In this paper, a delayed discrete Mittag-Leffler matrix function generated by two noncommutative square matrices is introduced. Utilizing this...
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An Investigation on Existence and Optimal Feedback Control for Fractional Neutral Stochastic Evolution Hemivariational Inequalities
This paper addresses some interesting results of optimal feedback control for neutral stochastic fractional systems in Hilbert spaces. We study the...
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Extended dissipative performance of fractional-order neural networks via LMI approach
This paper investigates the extended dissipativity performance of a specific category of fractional-order neural networks. The derivatives involving...
