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This manuscript established a comprehensive analysis of a general class of fractional order delay differential equations with Caputo-Fabrizio fractional derivative (CFFD). Functional analysis was used to examine the existence and uniqueness of the suggested class and to generate sufficient requirements for Ulam-Hyers (UH) type stability. Further, a numerical method based on Lagrange interpolation is used to compute approximate solution. Then, some applications in physical dynamics including a houseflies model and a Cauchy type problem were discussed to illustrate the established analysis with graphical illustrations.

This manuscript established a comprehensive analysis of a general class of fractional order delay differential equations with Caputo-Fabrizio fractional derivative (CFFD). Functional analysis was used to examine the existence and uniqueness of the suggested class and to generate sufficient requirements for Ulam-Hyers (UH) type stability. Further, a numerical method based on Lagrange interpolation is used to compute approximate solution. Then, some applications in physical dynamics including a houseflies model and a Cauchy type problem were discussed to illustrate the established analysis with graphical illustrations. [ABSTRACT FROM AUTHOR]

In this work, an epidemic model of a susceptible, exposed, infected and recovered SEIR-type is established for the distinctive dynamic compartments and epidemic characteristics of COVID-19 as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractional calculus known as piecewise derivatives. The existence theory is demonstrated through the establishment of sufficient conditions. In addition, result related to Hyers-Ulam stability is also derived for the considered model. A numerical method based on modified Euler procedure is also constructed to simulate the approximate solutions of the proposed model by employing various values of fractional orders. We testified the numerical results by using real available data of Japan. In addition, some results for the SEIR-type model are also presented graphically using the stochastic process, and the obtained results are discussed.

In this work, an epidemic model of a susceptible, exposed, infected and recovered SEIRtype is established for the distinctive dynamic compartments and epidemic characteristics of COVID-19 as it spreads across a population with a heterogeneous rate. The proposed model is investigated using a novel approach of fractional calculus known as piecewise derivatives. The existence theory is demonstrated through the establishment of sufficient conditions. In addition, result related to Hyers-Ulam stability is also derived for the considered model. A numerical method based on modified Euler procedure is also constructed to simulate the approximate solutions of the proposed model by employing various values of fractional orders. We testified the numerical results by using real available data of Japan. In addition, some results for the SEIR-type model are also presented graphically using the stochastic process, and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

Multiple sclerosis (MS) is a common neurological disorder that affects the central nervous system (CNS) and can cause lesions that spread over space and time. Our study proposes a mathematical model that illustrates the progression of the disease and its likelihood of recurrence. We use Caputo fractional-order (FO) derivative operators to represent non-negative solutions and to establish a steady-state point and basic reproductive number. We also employ functional analysis to prove the existence of unique solutions and use the Ulam-Hyres (UH) notion to demonstrate the stability of the solution for the proposed model. Furthermore, we conduct numerical simulations using an Euler-type numerical technique to validate our theoretical results. Our findings are presented through graphs that depict various behaviors of the model for different parameter values.

Multiple sclerosis (MS) is a common neurological disorder that affects the central nervous system (CNS) and can cause lesions that spread over space and time. Our study proposes a mathematical model that illustrates the progression of the disease and its likelihood of recurrence. We use Caputo fractional-order (FO) derivative operators to represent non-negative solutions and to establish a steady-state point and basic reproductive number. We also employ functional analysis to prove the existence of unique solutions and use the Ulam-Hyres (UH) notion to demonstrate the stability of the solution for the proposed model. Furthermore, we conduct numerical simulations using an Euler-type numerical technique to validate our theoretical results. Our findings are presented through graphs that depict various behaviors of the model for different parameter values. [ABSTRACT FROM AUTHOR]

In this research work, we establish some new results about piecewise equation involving Caputo Fabrizio derivative (CFD). The concerned class has been recently introduced and these results are fundamental for investigation of qualitative theory and numerical interpretation. We derive some necessary results for the existence, uniqueness and various form of Hyers-Ulam (H-U) type stability for the considered problem. For the required results, we need to utilize usual classical fixed point theorems due to Banach and Krasnoselskii's. Moreover, results devoted to H-U stability are derived by using classical tools of nonlinear functional analysis. Some pertinent test problems are given to demonstrate our results.

This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example.

The fundamental purpose of this research is to investigate the existence theory as well as the uniqueness of solutions to a coupled system of fractional order differential equations with Caputo derivatives. In this regard, we utilize the definition and properties of a newly developed conception of complex valued fuzzy rectangular b-metric spaces to explore the fuzzy form of some significant fixed point and coupled fixed point results. We further present certain examples and a core lemma in the case of complex valued fuzzy rectangular b-metric spaces.

In this paper, we establish a qualitative theory for implicit fractional order differential equations (IFODEs) with nonlocal initial condition (NIC) with delay term. Because area related to investigate existence and uniqueness of solution is important field in recent times. Also researchers are using existence theory to derive some prior results about a dynamical problem weather it exists or not in reality. In literature, we have different tools to study qualitative nature of a problem. On the same line the exact solution of every problem is difficult to determined. Therefore, we use technique of numerical analysis to approximate the solutions, where stability analysis is an important aspect. Therefore, we use a tool from non-linear analysis known as topological degree theory to develop sufficient conditions for existence and uniqueness of solution to the considered problem. Further, we also develop sufficient conditions for Hyers- Ulam type stability for the considered problem. To justify our results, we also give an illustrative example.

In this research work, we establish some new results about piecewise equation involving Caputo Fabrizio derivative (CFD). The concerned class has been recently introduced and these results are fundamental for investigation of qualitative theory and numerical interpretation. We derive some necessary results for the existence, uniqueness and various form of Hyers-Ulam (H-U) type stability for the considered problem. For the required results, we need to utilize usual classical fixed point theorems due to Banach and Krasnoselskii's. Moreover, results devoted to H-U stability are derived by using classical tools of nonlinear functional analysis. Some pertinent test problems are given to demonstrate our results. [ABSTRACT FROM AUTHOR]

This manuscript is devoted to investigate a class of multi terms delay fractional order impulsive differential equations. Our investigation includes existence theory along with Ulam type stability. By using classical fixed point theorems, we establish sufficient conditions for existence and uniqueness of solution to the proposed problem. We develop some appropriate conditions for different kinds of Ulam-Hyers stability results by using tools of nonlinear functional analysis. We demonstrate our results by an example. [ABSTRACT FROM AUTHOR]