In this article, a high-order time-stepping scheme based on the cubic interpolation formula is considered to approximate the generalized Caputo fractional derivative (GCFD). Convergence order for this scheme is
A model of gene regulatory networks with generalized proportional Caputo fractional derivatives is set up, and stability properties are studied. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are disc...
In this paper, we establish sufficient conditions for the existence of solutions for a nonlinear Langevin equation based on Liouville-Caputo-type generalized fractional differential operators of different orders, supplemented with nonlocal boundary c...
We investigate the existence and uniqueness results for coupled Langevin differential equations of fractional order with Katugampola integral boundary conditions involving generalized Liouville–Caputo fractional derivatives. Furthermore, we dis...
Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using
In this article, Euler’s technique was employed to solve the novel post-pandemic sector-based investment mathematical model. The solution was established within the framework of the new generalized Caputo-type fractional derivative for the syst...
The aim of this paper is to study the stability of generalized Liouville–Caputo fractional differential equations in Hyers–Ulam sense. We show that three types of the generalized linear Liouville–Caputo fractional differential equat...
Practical stability properties of generalized proportional Caputo fractional differential equations with bounded delay are studied in this paper. Two types of stability, practical stability and exponential practical stability, are defined and conside...
In this paper, nonlinear nonautonomous equations with the generalized proportional Caputo fractional derivative (GPFD) are considered. Some stability properties are studied by the help of the Lyapunov functions and their GPFDs. A scalar nonlinear fra...
The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physi...
A nonlocal boundary value problem for a couple of two scalar nonlinear differential equations with several generalized proportional Caputo fractional derivatives and a delay is studied. The exact solution of the scalar nonlinear differential equation...
In this article, we present some results on the existence and uniqueness of random solutions to a non-linear implicit fractional differential equation involving the generalized Caputo fractional derivative operator and supplemented with non-local and...
In this paper, a delayed reaction-diffusion neural network model of fractional order and with several constant delays is considered. Generalized proportional Caputo fractional derivatives with respect to the time variable are applied, and this type o...
An initial value problem for a scalar nonlinear differential equation with a variable order for the generalized proportional Caputo fractional derivative is studied. We consider the case of a piecewise constant variable order of the fractional deriva...
This paper deals with a new coupled system of integro-differential equations involving the generalized proportional Caputo derivatives equipped with nonlocal four-point boundary conditions. Sufficient criteria for the existence and uniqueness of solu...
We establish sufficient conditions for the existence of solutions for a nonlinear impulsive multi-order Caputo-type generalized fractional differential equation with infinite delay and nonlocal generalized integro-initial value conditions. The existe...
A scalar nonlinear impulsive differential equation with a delay and generalized proportional Caputo fractional derivatives (IDGFDE) is investigated. The linear boundary value problem (BVP) for the given fractional differential equation is set up. The...
The nonlinear fractional-order model of bioethanol production under a generalized nonlocal operator in the Caputo sense is investigated in this work. Theoretical and computational aspects of the considered model are discussed. We prove that the model...
Under different criteria, we prove the existence of solutions for sequential fractional differential inclusions containing Riemann–Liouville and Caputo type derivatives and supplemented with generalized fractional integral boundary conditions....
In this paper, we investigate a class of fuzzy partially differentiable models for Caputo–Hadamard-type Goursat problems with generalized Hukuhara difference, which have been widely recognized as having a significant role in simulating and anal...
Herein, we developed and analyzed a new fractal–fractional (FF) operational matrix for orthonormal normalized ultraspherical polynomials. We used this matrix to handle the FF Riccati differential equation with the new generalized Caputo FF derivative...
The present study investigates the generalized dispersion of a solute in an incompressible MHD flow via a rectangular channel with injectable or suctioned walls. The mathematical model of dispersion suggests a distinct type of mass flux expressed as...
The synchronization problem for impulsive fractional-order Cohen–Grossberg neural networks with generalized proportional Caputo fractional derivatives with changeable lower limit at any point of impulse is studied. We consider the cases when th...
In this paper an algorithm for approximate solving of a boundary value problem for a nonlinear differential equation with a special type of fractional derivative is suggested. This derivative is called a generalized proportional Caputo fractional der...
In this study, we introduced the
The purpose of this paper is to investigate a class of novel symmetric coupled fuzzy fractional partial differential equation system involving the Caputo–Katugampola (C-K) generalized Hukuhara (gH) derivative. Within the framework of C-K gH dif...
This study investigates two fractional differential equation systems defined using the recently introduced generalized Caputo-type fractional derivatives and the Mittag-Leffler functions, which play a significant role among special functions. The ana...
In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equat...
The current study is devoted to investigating the existence and uniqueness of solutions for a new class of symmetrically coupled system of nonlinear hyperbolic partial-fractional differential equations in generalized Banach spaces in the sense of
This manuscript investigates the existence, uniqueness and Ulam–Hyers stability (UH) of solution to fractional differential equations with non-instantaneous impulses on an arbitrary domain. Using the modern tools of functional analysis, we achi...
In this article, the numerical adaptive predictor corrector (Apc-ABM) method is presented to solve generalized Caputo fractional initial value problems. The Apc-ABM method was utilized to establish approximate series solutions. The presented techniqu...
This paper delves into a novel category of nonlocal boundary value problems concerning nonlinear sequential fractional differential equations, coupled with a unique form of generalized Riemann–Liouville fractional differential integral boundary...
In this paper, we investigate the existence and Hyers–Ulam stability of a coupled differential equations of fractional-order with multi-point (discrete) and integral boundary conditions that are related to Katugampola integrals. This manuscript...
In this study, we perform a dynamical analysis of a generalized tumor model using the Caputo fractional-order derivative. Tumor growth models are widely used in biomedical research to understand the dynamics of tumor development and to evaluate poten...
This study focuses on the solution of the rotationally symmetric Rossler attractor by using the adaptive predictor–corrector algorithm (Apc-ABM-method) and the fractional Laplace decomposition method (
In this article, by combining a recent critical point theorem and several theories of the ψ-Caputo fractional operator, the multiplicity results of at least three distinct weak solutions are obtained for a new ψ-Caputo-type fractional differe...
We develop the existence criteria for solutions of Liouville–Caputo-type generalized fractional differential equations and inclusions equipped with nonlocal generalized fractional integral and multipoint boundary conditions. Modern techniques o...
A generalized proportional vector-order fractional derivative in the Caputo sense is defined and studied. Two types of existence results for the mild solutions of the initial value problem for nonlinear Caputo-type generalized proportional vector-ord...
The primary aim of this study is to establish new Wirtinger-type inequalities involving fractional derivatives, which are essential tools in analysis and applied mathematics. We derive generalized Wirtinger-type inequalities incorporating the
This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized
Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differenti...
In this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In t...
This paper presents a finite difference method for solving the Caputo generalized time fractional diffusion equation. The method extends the
In this study, we address a coupled system of nonlinear fractional delay differential equations subject to cross-coupled multi-point boundary conditions. By utilizing the generalized power Caputo fractional derivative, we present a unified theoretica...
We study the existence and uniqueness of solutions for coupled Langevin differential equations of fractional order with multipoint boundary conditions involving generalized Liouville–Caputo fractional derivatives. Furthermore, we discuss Ulam&n...
In this paper, the existence of a unique solution is established for a coupled system of Langevin fractional problems of
The aim of this research work is to derive some appropriate results for extremal solutions to a class of generalized Caputo-type nonlinear fractional differential equations (FDEs) under nonlinear boundary conditions (NBCs). The aforesaid results are...
The fuzzy fractional differential equation explains more complex real-world phenomena than the fractional differential equation does. Therefore, numerous techniques have been timely derived to solve various fractional time-dependent models. In this p...
This paper introduces a fractional generalization of the classical Legendre differential equation based on the Atangana–Baleanu–Caputo (ABC) derivative. A novel fractional Legendre-type operator is rigorously defined within a functional f...
Integral inequalities have accumulated a comprehensive and prolific field of research within mathematical interpretations. In recent times, strategies of fractional calculus have become the subject of intensive research in historical and contemporary...
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