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Calculus and Integral Transforms
In the calculus course, the solutions of limit, differentiation, integrals, series and series approximations of given functions are mainly studied....
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Integral Calculus for Engineers
The book mainly deals with basic concepts and examples about integral calculus such as indefinite integral, definite integral, improper integrals,...
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Multivariate Integral Calculus
Multivariate integral calculus is addressed. For two–dimensional spaces, we introduce line integrals and show under what conditions a line integral...
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Integral Calculus
We introduce two important notions: (i) the integral of a function (related to the area under its graph), and (ii) the primitive of a function...
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Differential and Integral Calculus for Fuzzy Number-Valued Functions with Interactivity
This chapter presents the theory of differential and integral calculus for autoregressive fuzzy processes, that is, fuzzy number-valued functions F...
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Introduction to Fractional Calculus
At the beginning of the development of the theory of classical calculus (called integer-order calculus in this book), the British scientist Isaac...
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Progress on Generalized Hilfer Fractional Calculus and Fractional Integral Inequalities
After motivation we give a complete background on needed \(\psi \)...
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Elements of the Calculus of Variations
ThisCalculus of variations chapter explains the basic principles of the theory of the calculus of variations. Having defined what a functional is,...
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Wiener Path Integral Formalism
This chapter introduces the path integral as a mathematical tool with the potential to address some of the current challenges in stochastic...
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Integral Theorems and Differential Forms
This chapter contains two sections. The first section deals with well-known theorems involving integrals of tensorial field variables to complete...
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Bicomplex Mittag-Leffler Function and Applications in Integral Transform and Fractional Calculus
Motivated by the importance of the applications of the Mittag-Leffler functions in many areas of engineering and applied science, efforts have been...
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Definitions and Numerical Evaluations of Fractional Calculus
As previously noted, fractional calculus dates back to the days when Newton and Leibniz first invented traditional calculus. In the absence of a...
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Mikusiński’s Operational Calculus Applied in General Classes of Fractional Calculus
Mikusiński’s operational calculus is an algebraic formalism for integral and derivative operators, constructed in the mid 20th century, which can be...
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Intelligent predictive computing for functional differential system in quantum calculus
The aim of this study is to present a novel application of Levenberg–Marquardt backpropagation (LMB) to investigate numerically the solution of...
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Formation control of nonholonomic wheeled mobile robots via fuzzy fractional-order integral sliding mode control
This paper presents a robust formation control scheme for a team of nonholonomic wheeled mobile robots. First, the formation kinematic controller is...
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Transient high-frequency spherical wave propagation in porous medium using fractional calculus technique
Transient high-frequency spherical wave propagation in the porous medium is studied using the Biot-JKD theory. The porous media is considered to be a...
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Multiplicative Integral Theory of Generalized Orthopair Fuzzy Sets and Its Applications
There are two main issues of fuzzy multi-attribute decision-making: determine the weight of each attribute and choose an appropriate aggregation...
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Practical algebraic calculus and Nullstellensatz with the checkers Pacheck and Pastèque and Nuss-Checker
Automated reasoning techniques based on computer algebra have seen renewed interest in recent years and are for example heavily used in formal...
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Trefftz co-chain calculus
We are concerned with a special class of discretizations of general linear transmission problems stated in the calculus of differential forms and...
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Approximate Solutions: The Integral Method
There are various situations where it is desirable to obtain approximate analytic solutions. An obvious case is when an exact solution is not...