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A Class of Fractional Integral Operators Involving a Certain General Multiindex Mittag-Leffler Function
The paper is essentially motivated by the demonstrated potential for applications of the presented results in numerous widespread research areas,...
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The Prabhakar Fractional q-Integral and q-Differential Operators
In this short note, we discuss the joint work (Shaimardan et al., The Prabhakar fractional q-integral and q-differential operators, and their...
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Generalized fractional Dirac type operators
We introduce a class of fractional Dirac type operators with time variable coefficients by means of a Witt basis, the Djrbashian–Caputo fractional...
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Approximation and convergence of generalized fractional Sturm-Liouville problem via integral form
The aim of this study is to present a numerical algorithm for solving the generalized fractional Sturm-Liouville differential equation. We define the...
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Study on Hermite-Hadamard-type inequalities using a new generalized fractional integral operator
In this study, a new definition of the fractional integral operator is first proposed, which generalizes some well-known fractional integral...
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An explanation on four new definitions of fractional operators
Fractional calculus has drawn more attentions of mathematicians and engineers in recent years. A lot of new fractional operators were used to handle...
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Fractional Differential and Integral Operators
Fractional differentiation and integration have witness a continuous revolution in the last decades as they have been found to capture behaviors that...
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Inverse Coefficient Problems for a Time-Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative
AbstractThis paper considers the inverse problem of determining the time-dependent coefficient in the fractional wave equation with Hilfer...
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Inverse Coefficient Problem for Fractional Wave Equation with the Generalized Riemann–Liouville Time Derivative
This paper considers the inverse problem of determining the time-dependent coefficient in the fractional wave equation with Hilfer derivative. In...
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Controllability Results of Hilfer Fractional Derivative Through Integral Contractors
The paper sheds light on Hilfer’s controllability facts of neutral fractional system. Originally, the mild solution is derived using semigroup theory...
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Stability Analysis and Existence Criteria with Numerical Illustrations to Fractional Jerk Differential System Involving Generalized Caputo Derivative
This inquire about ponder is committed to investigating a few properties in connection to behaviors of solutions to an extended fractional structure...
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Generalized Fractional Differential Systems with Stieltjes Boundary Conditions
In this work, we study the existence of solutions to a new class of boundary value problems consisting of a system of nonlinear differential...
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Parameterized Inequalities of Different Types for Preinvex Functions with Respect to another Function via Generalized Fractional Integral Operators and their Applications
We prove an identity with two parameters for a function differentiable with respect to another function via generalized integral operator. By...
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Existence and Stability of Integro Differential Equation with Generalized Proportional Fractional Derivative
AbstractIn this study, integro-differential equations of arbitrary order are studied. The fractional order is expressed in terms of the
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On the analysis of fractional calculus operators with bivariate Mittag Leffler function in the kernel
Bivariate Mittag-Leffler (ML) functions are a substantial generalization of the univariate ML functions, which are widely recognized for their...
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A Pro Rata Definition of the Fractional-Order Derivative
In this paper a novel definition of the fractional-order derivative operator will be introduced. This operator will be called “pro rata” due to its...
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An Inverse Source Problem for Anomalous Diffusion Equation with Generalized Fractional Derivative in Time
The inverse problem of recovering a source term along with diffusion concentration for a generalized diffusion equation has been considered. The...
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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...
